Answer:
a) 64.06% probability that he is through grading before the 11:00 P.M. TV news begins.
b) The hardness distribution is not given. But you would have to find s when n = 39, then the probability would be 1 subtracted by the pvalue of Z when X = 51.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sum of n trials, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
In this question:
[tex]n = 48, \mu = 48*5 = 240, s = 4\sqrt{48} = 27.71[/tex]
These values are in minutes.
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
From 6:50 PM to 11 PM there are 4 hours and 10 minutes, so 4*60 + 10 = 250 minutes. This probability is the pvalue of Z when X = 250. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{250 - 240}{27.71}[/tex]
[tex]Z = 0.36[/tex]
[tex]Z = 0.36[/tex] has a pvalue of 0.6406
64.06% probability that he is through grading before the 11:00 P.M. TV news begins.
(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?
The hardness distribution is not given. But you would have to find s when n = 39(using the standard deviation of the population divided by the square root of 39, since it is not a sum here), then the probability would be 1 subtracted by the pvalue of Z when X = 51.
What is the solution of √1-3x = x+3 ?
Answer:
{-1, -8}
Step-by-step explanation:
Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".
Squaring both sides of the given equation, we get:
1 - 3x = x^2 + 6x + 9, or x^2 + 6x + 8 + 3x, or
x^2 + 9x + 8 = 0. Factoring, we get: (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.
Answer:
I hope the given equation is :
{-1, -8}
First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,
1 - 3x = (x + 3)²
1 - 3x = (x + 3)*(x + 3) Since a² = a * a
1 - 3x = x² + 3x + 3x + 3² By multiplication.
1 - 3x = x² + 6x + 9 Combine the like terms.
x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation
x² + 9x + 8 = 0 Combine the like terms.
Next step is to factor the trinomial to solve the above equation for x.
For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.
So, 8 = 1 * 8
Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,
x² + 1x + 8x + 8 = 0
(x² + 1x) + (8x + 8) = 0 Group the terms.
x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.
(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).
So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.
Hence, x = -1 and - 8.
Next step is to plug in -1 and -8 in the original equation to cross check the solutions.
For x = -1,
Simplify each sides separately.
2 = 2
2 = 2 is correct. So, x = -1 satisfy the equation.
Hence, x = -1 is the real solution of the given equation.
Similarly let's plug in x = -8 now. So,
Simplify each sides separately.
5 = 2
5 = 2 is not true. So, x = -8 is the extraneous solution.
Therefore, the only solution is x = -1.
Hence, the correct choice is C.
Hope this helps you!
Step-by-step explanation:
mark brainlies plssssssssss
The checking accounts of USF Credit Union are categorized by age of account and balance in account. We are going to select an account at random from this group of 2000 accounts.What is the conditional probability that the account has a balance at least $500, given that it is at least 3 years old, that is P(>=$500 | >=3 years)?
a. 1/2
b. 1/10
c. 1/4
d. None of these
Missing details to question is attached
Answer:
c) [tex] \frac{1}{4} [/tex]
Step-by-step explanation:
S
Required:
Find the probability that the account has a balance at least $500, given that it is at least 3 years old.
Which means: P(≥$500 | ≥3 years)
To find the probability, use the formula below:
P(≥$500 | ≥3 years) = (No. of accounts with balance≥ 500 and age ≥3 years) / (No. of accounts with age≥3 years)
Where from th given information:
Number of accounts with balance≥ 500 and age ≥3 years = 200
Number of accounts with age≥3 years = 600 + 200 = 800
Therefore,
P(≥$500 | ≥3 years) [tex] = \frac{200}{800} = \frac{1}{4} [/tex]
The probability that the account has a balance at least $500, given that it is at least 3 years old = [tex] \frac{1}{4} [/tex]
Need help please :) thanks
Please help ASAP
April runs at a rate of 25 feet per second for 11 seconds. Determine how far she
traveled and select the appropriate units to describe it.
She traveled ___________
Isaac drove on the interstate for 3 hours and traveled a total of 165 miles.
Determine his rate of travel and select the appropriate units to describe it.
He traveled ___________
Answer:
1. distance = 275 ft
2. rate = 55 miles/hour
Step-by-step explanation:
April travels at the rate of 25 ft per seconds and the time she spent traveling is 11 seconds. How far she traveled is the distance she covered. The rate or the speed unit is given as ft per seconds. Therefore, the distance covered can be expressed as follows.
rate = distance/time
where
rate = 25 ft/sec
time = 11 secs
rate = distance/time
25 = distance/11
cross multiply
distance = 25 × 11
distance = 275 ft
Isaac drove for 3 hours and he covered a distance of 165 miles. The rate of travel can be expressed as follows
rate = distance/time
distance = 165 miles
time = 3 hours
rate = 165/3
rate = 55 miles/hour
Dylan paid a plumber $120 for 4 hours of labor. How much does the plumber charge per hour of labor? A. $15 per hour B. $30 per hour C. $116 per hour D. $480 per hour stay safe!
Answer:
Brainleist :)
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
B) 30 dollars for 1 hour of labor
answe:
B) 30 dollars for 1 hour of labor
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
important messagee:
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The cost (in dollars) of producing x units of a certain commodity is C(x) = 7000 + 6x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) x = 103 $ per unit (ii) x = 101 $ per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit
Answer:
The instantaneous rate is 36.
Step-by-step explanation:
Given the cost of producing a commodity,
[tex]C(x) = 7000 + 6x + 0.15x^{2}[/tex]
Now calculate the average rate of change in cost of producing commodity.
Use below formula to calculate average rate of change when (i) x = 103 $ per unit:
[tex]\text{Average rate of change} = \frac{C(103) – C(100) }{103 - 100} \\C(x) = 7000 + 6x + 0.15x^{2} \\C(100) = 7000 + 6 \times 100 + 0.15 (100)^{2} = 9100 \\C(103) = 7000 + 6 \times 103 + 0.15 (103)^{2} = 9209.35 \\\text{Average rate of change} = \frac{9209.35 - 9100}{103 - 100} = 36.45[/tex]
Now calculate average rate of change when (ii) x = 101 $ per unit:
[tex]\text{Average rate of change} = \frac{C(101) – C(100) }{101 - 100} \\C(x) = 7000 + 6x + 0.15x^{2} \\C(100) = 7000 + 6 \times 100 + 0.15 (100)^{2} = 9100 \\C(101) = 7000 + 6 \times 101 + 0.15 (101)^{2} = 9136.15 \\\text{Average rate of change} = \frac{9136.15 - 9100}{101 - 100} = 36.15[/tex]
Now to find the Instantaneous Rate of Change we just need to find the differentiation of given function.
[tex]C(x) = 7000 + 6x + 0.15x^{2} \\C’(x) = 6 + 0.3x \\[/tex]
Instantaneous Rate of Change when x = 100
[tex]= 6 + 0.3 \times (100) \\= 36[/tex]
Solve the following and
make sure to write your
answer in scientific
notation.
(1.5 x 105)(5 x 103)
Answer:
7.5* 10^8
Step-by-step explanation:
(1.5 x 10^5)(5 x 10^3)
Multiply the numbers
1.5*5=7.5
Add the exponents
10 ^(5+3) = 10^8
Put back together
7.5* 10^8
This is in scientific notation
If a coin is tossed 5 times, and then a standard six-sided die is rolled 4 times, and finally a group of three cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answer: 5,499,187,200
Step-by-step explanation:
A coin is tossed 5 times.
There are two options (heads or tails) so the possible outcomes are: 2⁵
A six-sided die is rolled 4 times.
There are six options so the possible outcomes are: 6⁴
A group of 3 cards are drawn (without replacement).
The first outcome has 52 options, the second has 51 options, and the third has 50 options: 52 x 51 x 50
Now if we want the coin AND the die AND the cards, we have to multiply all of their possible outcomes:
2⁵ x 6⁴ x 52 x 51 x 50
= 32 x 1296 x 132,600
= 5,499,187,200
Evaluate f(x) = x2 + 1 for f(-1)
Answer: -1
Step-by-step explanation:
to calculate f(-1), you know that x = -1. so all you have to do is substitute:
f(-1) = (-1)2 + 1
f(-1) = -2 + 1
f(-1) = -1
Answer:
0
Step-by-step explanation:
What is the greatest number that can be divided evenly into 78 and 104 without leaving a remainder?
Answer:
26 can be divides evenly into 78 and 104 without leaving a remainder
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
78= 2 × 3 × 13
104= 2 × 2 × 2 × 13
The required number is: 2 × 13= 26
Please answer this correctly without making mistakes
Answer:
7
Step-by-step explanation:
hh
ht
th
tt
so it's a 1/4 chance
1/4 * 28 = 7
Answer:
7
Step-by-step explanation:
The probability of both coins landing on heads is:
1/2 × 1/2 = 1/4
Multiply by 28.
1/4 × 28
= 7
Emily worked only 4/5 of her normal 40-hr work week. If she makes $18 per hour, how much money did she earn for the week? Use the equation
Answer:
576 for the week
Step-by-step explanation:
First determine how many hours she worked
4/5 * 40 = 32 hours
32 hours times the hourly rate of 18
32*18 =576
Which are true of the function f(x)=49(1/7)?select three options. A)The domain is the set of all real numbers. B) the range is the set of all real numbers. C) the domain is x >0. D)the range is y>0. E)as increases by 1, each y value is one -seventh of the previous y-value.
Answer:
A,D and E
Step-by-step explanation:
We are given that a function
[tex]f(x)=49(\frac{1}{7})^x[/tex]
The given function is exponential function .
The exponential function is defined for all real values of x.
Therefore, domain of f=Set of all real numbers
Substitute x=0
[tex]y=f(0)=49>0[/tex]
Range of f is greater than 0.
x=1
[tex]y(1)=\frac{49}{7}[/tex]
x=2
[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]
As x increases by 1, each value of y is one-seventh of the previous y-value.
Therefore, option A,D and E are true.
Answer:
A D E
Step-by-step explanation:
Edge2020 quiz
Which of the x-values are solutions to the following inequality? 17 > x Choose all answers that apply: (A) x = 7 (B) x = 12 (C) x = 17
Answer:
7 and 12
Step-by-step explanation:
7 and 12 are ok
17 is not
hope this helps
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The inequality is given below.
x < 17
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?
Work Shown:
log(200) = log(2^3*5^2)
log(200) = log(2^3) + log(5^2)
log(200) = 3*log(2) + 2*log(5)
log(200) = 3*q + 2*p
log(200) = 2p + 3q
The log rules I used were
log(A*B) = log(A)+log(B)
log(A^B) = B*log(A)
The equivalent expression of log(200) is 2p + 3q
The logarithmic expression is given as:
[tex]\mathbf{log 200}[/tex]
Rewrite as:
[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]
Express as exponents
[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]
Split
[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]
Apply law of logarithms
[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]
From the question;
log(5) = p and log(2) = q
So, we have:
[tex]\mathbf{log(200) = 2p +3q}[/tex]
Hence, the equivalent expression of log(200) is 2p + 3q
Read more about logarithmic expressions at:
https://brainly.com/question/9665281
4. The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Answer:
5in³Step-by-step explanation:
The question is in complete. Here is the complete question.
"The dimensions of a triangular pyramid are shown below. The height of
the pyramid is 6 inches. What is the volume in cubic inches?
Base of triangle = 1in
height of triangle = 5in"
Given the dimension of the triangular base of base 1 inch and height 5inches with the height of the pyramid to be 6inches, the volume of the triangular pyramid is expressed as [tex]V = \frac{1}{3}BH[/tex] where;\
B = Base area
H = Height of the pyramid
Base area B = area of the triangular base = [tex]\frac{1}{2}bh[/tex]
b = base of the triangle
h = height of the triangle
B = [tex]\frac{1}{2} * 5 * 1\\[/tex]
[tex]B = 2.5in^{2}[/tex]
Since H = 6inches
Volume of the triangular pyramid = [tex]\frac{1}{3} * 2.5 * 6\\[/tex]
[tex]V = 2.5*2\\V =5in^{3}[/tex]
given a 60 month car loan at 4.71%, explain how much your monthly payments would be for a $18,400 car and what your TOTAL COST would be given that interest.
Answer:
$23161.10
Step-by-step explanation:
Assuming this is compounded annually, we use our simple interest rate formula: A = P(1 + r)^t
Step 1: Convert months to years
60 months/12 month/year = 5 years
Step 2: Plug in known variables
A = 18400(1 + 0.0471)^5
Step 3: Solve
When you plug step 2 into your calc you should get 23161.1 as your answer. I am assuming that this isn't compounded quarterly or monthly, but just yearly.
Which will provide the largest yield on an annuity after 30 years with 6% annual interest, compounded monthly? Annuity A: Deposit $2400 per year. Annuity B: Deposit $600 per quarter. Annuity C: Deposit $72,000 one lump sum.
Answer:
Annuity C: Deposit $72,000 one lump sum
Step-by-step explanation:
The yield is improved when the money is on deposit for a longer period.
If the $2400 annual deposit is made at the first of the year, then it will yield more than $600 deposits made at the first of each quarter.
If the $72,000 deposit is made at the beginning of the period, the entire amount is earning interest for the entire period.
Annuity C will provide the largest yield.
Rhea obtained a CO-OP credit working at a computer store. They have now hired her for a summer job with the store. She makes $8/hour, plus a 5% commission on sales.
Which expression best describes Rhea's total earnings? Explain.
a) E = 8h + 5s b) E = 8h + .50s
c) E = 8h + .005s d) E = 8h + 0.05s
Rhea worked 15 hours last week and made $260 in total. What were her total sales in computers for the week?
Why do you think employers offer commissions to their employees? Do you think there are any potential problems with this form of earnings?
Answer:
d) E = 8h + 0.05s
Her total sales in computers for the week is $2800.
Step-by-step explanation:
Let Rhea's hourly pay =h
She makes $8/hour, therefore sales for h hours =$8h
Let the volume of sales = s
She also earns 5% commission on sales = 5% of s = 0.05s
Therefore, the expression which best describes Rhea's total earnings:
(D) E=8h+0.05s
Rhea worked 15 hours last week and made $260 in total.
h=$15
From the formula
260=8(15)+0.05s
0.05s=260-8(15)
0.05s=140
s=2800
Her total sales in computers for the week is $2800.
Employers offer commissions to their employees to motivate them to seek to make sales rather than just passing time.
In so far as the sales commission do not eat up the profit of the business, there are no potential problems with this form of earnings
AC is tangent to circle O at point C. What is the measure of angle ACO?
Answer:
m < ACO = 90 degrees.
Step-by-step explanation:
The line joining the center O of the circle to the point of contact of the tangent is a right angle.
Answer: 90 degrees
Step-by-step explanation: Khan academy
Multiple(x-4)(2x+3) using the distributive property
Answer:
See Below
Step-by-step explanation:
x(2x) - 4(2x) + x(3) - 4(3)
= 2x² - 8x + 3x -12
= 2x²-5x-12
Solve for x in the equation x squared minus 4 x minus 9 = 29. x = 2 plus-or-minus StartRoot 42 EndRoot x = 2 plus-or-minus StartRoot 33 EndRoot x = 2 plus-or-minus StartRoot 34 EndRoot x = 4 plus-or-minus StartRoot 42 EndRoot
Answer:
[tex]x=2$\pm$\sqrt{42}[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^{2} -4x-9=29\\\Rightarrow x^{2} -4x-9-29=0\\\Rightarrow x^{2} -4x-38=0[/tex]
Formula:
A quadratic equation [tex]ax^{2} +bx+c=0[/tex] has the following roots:
[tex]x=\dfrac{-b+\sqrt D}{2a}\ and\\x=\dfrac{-b-\sqrt D}{2a}[/tex]
Where [tex]D= b^{2} -4ac[/tex]
Comparing the equation with [tex]ax^{2} +bx+c=0[/tex]
a = 1
b = -4
c= -38
Calculating D,
[tex]D= (-4)^{2} -4(1)(-38)\\\Rightarrow D = 16+152 = 168[/tex]
Now, finding the roots:
[tex]x=\dfrac{-(-4)+\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4+2\sqrt {42}}{2}\\\Rightarrow x=2+\sqrt {42}\\and\\x=\dfrac{-(-4)-\sqrt {168}}{2\times 1}\\\Rightarrow x=\dfrac{4-2\sqrt {42}}{2}\\\Rightarrow x=2-\sqrt {42}[/tex]
So, the solution is:
[tex]x=2$\pm$\sqrt{42}[/tex]
Answer is A or the first one
As part of a physics experiment, Ming drops a baseball from the top of a 315-foot building. To the nearest tenth of a second, for how many seconds will the baseball fall? (Hint: Use the formula h = 16t^2, which gives the distance h, in feet, that a free-falling object travels in t seconds.)
Answer: 4.4 seconds
Step-by-step explanation:
h(t) = -16t² + 315
Since we want to find the total time the baseball is in the air, we need to find the time (t) when the ball lands on the ground --> h(t) = 0
0 = -16t² + 315
-315 = -16t²
[tex]\dfrac{315}{16}=t^2\\\\\\\sqrt{\dfrac{315}{16}}=t\\\\\\\dfrac{\sqrt{315}}{4}=t\\\\\\\large\boxed{4.4=t}[/tex]
Answer:
≈ 4.44 sec
Step-by-step explanation:
h= 315 ft
h= 16t²
315 = 16t²
t²=315/16
t=√315/16 ≈ 4.44 sec
Find the surface area of a sphere with a diameter 12 cm. Round your answer to the nearest whole number
Answer:
SA = 144π or 452 cm
Step-by-step explanation:
Surface area of a sphere: SA = 4πr²
To find r radius, we simply divide diameter by 2 to get r = 6. Now we simply plug in 6:
SA = 4π(6)²
SA = 4π36
SA = 144π or 452.389
Answer:
144pi
Step-by-step explanation:
calculator
represent 5 20 30 25 10 on a pie chart
Answer :
I have solved for the points.
Explanation :
Just get a protractor and plot out the angles into a circle. Starting with the largest angle.
Explain how to translate the statement into an equation. Use n for the variable. Thirteen less than a number is four EXPLAIN:
start here
Answer:
13-n=4
Subtract both sides by 13
-n=-9
n=9
Step-by-step explanation:
13 less means - and a number means n that you don’t know. is means = sign. And so we get the answer that I gave you. Thank you
PLEASE I NEED HELP ASAP
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
A 11 gram sample of a substance that's
used to treat thyroid disorders has a k-
value of 0.1247.
Enter the correct answer.
N = Noekt
DONE
No = initial mass (at time t = 0)
ĐOO
t?
N = mass at time t.
k = a positive constant that depends on
the substance itself and on the units
used to measure time
t = time, in days
Answer: 55.6 days
Step-by-step explanation:
[tex]P=P_oe^{kt}\\\\\bullet \quad P=\dfrac{1}{2}P_0\\\bullet \quad k=-0.1247\\\bullet \quad t = unknown\\\\\\\dfrac{1}{2}P_o=P_oe^{-0.1247t}\\\\\\\dfrac{1}{2}=e^{-0.1247t}\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=-0.1247t\\\\\\\dfrac{ln\dfrac{1}{2}}{-0.1247}= t\\\\\\\large\boxed{55.6=t}[/tex]
Brian set a goal to horseback ride more than 6 miles. The horse he rode averaged a speed of 4.6 miles per hour. A 2-column table with 4 rows titled Brian's Activity time (hours). Column 1 has entries hiking, mountain biking, horseback riding, cross-country skiing. Column 2 has entries 3, 1.45, 1.2, 0.75. Brian rode miles. Did he reach his goal?
Answer:
BRIAN DID NOT REACH HIS GOAL! Brian rode 5.52 miles!
Step-by-step explanation:
Answer:
he didn't reach his goal. he rode 5.52 miles
Step-by-step explanation:
9-3x is greater than or equal to 2(x-3)
Answer:
x≤3
Step-by-step explanation:
9-3x≥2(x-3)
9-3x≥2x-6
-3x-2x≥-6-9
-5x≥-15
-5x/-5≥-15/-5
x≤3
A marketing team is targeting people who might buy a hybrid car. In their city, with a population of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
Answer:
The population proportion is 0.1057.
For samples of size n: Mean = 0.1057, Standard deviation [tex]s = \frac{0.3075}{\sqrt{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem for Proportions:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Population proportion:
Of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one.
This means that [tex]p = \frac{3170}{30000} = 0.1057[/tex]
The population proportion is 0.1057.
Mean and standard deviation of the sampling distribution for samples of size n
By the Central Limit Theorem, the mean is [tex]\mu = p = 0.1057[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{0.1057*0.8943}{n}} = \frac{0.3075}{\sqrt{n}}[/tex]