Answer:
0.0526 = 5.26% probability that 32 filtered cigarettes have a mean of 19.2 mg or less.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using 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.
Given that the tar content of cigarettes have a mean of 20.1 mg and a standard deviation of 3.15 mg
This means that [tex]\mu = 20.1, \sigma = 3.15[/tex]
Sample of 32 filtered cigarettes
This means that [tex]n = 32, s = \frac{3.15}{\sqrt{32}} = 0.5568[/tex]
What is the probability that 32 filtered cigarettes have a mean of 19.2 mg or less?
This is the pvalue of Z when X = 19.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{19.2 - 20.1}{0.5568}[/tex]
[tex]Z = -1.62[/tex]
[tex]Z = -1.62[/tex] has a pvalue of 0.0526
0.0526 = 5.26% probability that 32 filtered cigarettes have a mean of 19.2 mg or less.
can someone help I need to fill in the blank
Answer:
240
Step-by-step explanation:
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 45 degrees at midnight and the high and low temperature during the day are 54 and 36 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
Answer:
D = 9sin(2π(t + a)/24) + 45
Step-by-step explanation:
Let's find the average temperature;
(54 + 36)/2 = 45°
Amplitude = 54 - 45 = 9
From the wave equation, we can write the temperature as;
D = 9sin(2π(t + a)/24) + 45
Where;
D is the temperature
t is the time in hours after midnight
a is a "phase" that is used to set the time at which temperature(D) occurs
A veterinarian prescribed Christy, a 31-pound dog, an antibacterial medication in case an infection emerges after her teeth were cleaned. If the dosage is 8.75 mg for every pound, how much medicine was given?
Answer:
271.25 mg
Step-by-step explanation:
The amount of medicine will be equal to 271.25 mg.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that a veterinarian prescribed Christy, a 31-pound dog, an antibacterial medication in case an infection emerges after her teeth were cleaned. The dosage is 8.75 mg for every pound.
The amount of medicine will be calculated as below:-
Amount = 31 x 8.75
Amount = 271.25 mg
Therefore, the amount of medicine will be equal to 271.25 mg.
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In a filling line at A & C Foods, Ltd., the mean fill volume for rice bubbles is 475 grams and the standard deviation is 10 grams. The design specifications are [450, 495] grams. Any output outside of design specifications is treated as non-conforming. (1) Calculate the dpmo of the process (by calculating the area of non-conformance). Please type your answer in integers.
Answer:
The dpmo of the process is of 29000
Step-by-step explanation:
Dpmo of a process:
The dpmo of a process is the number of defects per million opportunities.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
In this question:
First, using the normal distribution, we calculate the proportion of defective bubbles. Then, using this proportion, we calculate the dpmo.
Mean fill volume for rice bubbles is 475 grams and the standard deviation is 10 grams.
This means that [tex]\mu = 475, \sigma = 10[/tex]
The design specifications are [450, 495] grams. Any output outside of design specifications is treated as non-conforming.
Below 450 and Above 495 are non-conforming.
Below 450:
The proportion is the pvalue of Z when X = 450. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{450 - 475}{10}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
Above 495:
The proportion is 1 subtracted by the pvalue of Z when X = 495. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{495 - 475}{10}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
The proportion of defectives is 0.0228 + 0.0062 = 0.0290
Dpmo:
Number of defects per million, that is, the proportion multiplied by 1000000.
1000000*0.0290 = 29000
The dpmo of the process is of 29000
I GIVE BRAINLIEST FOR RIGHT ANSWER AND EXPLANATION
Mrs. Evans opens a bank account and starts to gain money at a constant rate of $3 per day. What is the total amount of money that she will gain after a week?
Answer:
$21
Step-by-step explanation:
Samir just finished renovating a house during the renovation he added a steel beam as a support the steel beam was 15 feet long and cost $135 complete the statement by selecting the correct dollar amount from the provided list
the cost of the beam was _______per yard
Answer:
$27
Step-by-step explanation:
According to your question. The complete cost was $135 for a fifteen feet long beam. If you are looking for the price per yard, a yard has three feet, therefore in fifteen feet, there are five yards.
15 divided into 3 equals 5
$135 divided into five equals $27
I hope this helps.
According to the recent poll, 22 1/4% of the people polled said that they approved of the city plan to expand the library. If 1004 people was polled, about how many were in favor of the expansion?
Answer:
Some 224 people were in favor of the expansion.
Step-by-step explanation:
Given that, according to the recent poll, 22 1/4% of the people polled said that they approved of the city plan to expand the library, if 1004 people was polled, to determine how many were in favor of the expansion should be done the following calculation:
1/4 = 0.25
100 = 1004
22.25 = X
1004 x 22.25 / 100 = X
223.39 = X
Thus, some 224 people were in favor of the expansion.
Find the area of the shaded portion below.
Step-by-step explanation:
the area of the half-circle:
πr² /2= 3.14* 20² /2= 3.14 * 400 /2 =1256/2=628cm²
50*80/2=2000cm²
Shaded area:
2000-628=1372cm²
Answer:
Step-by-step explanation:
The shaded area is a trapezoid minus the area of half a circle.
T=h(b1+b2)/2
T=40(50+80)/2
T=2600cm^2
Now the area of the half circle
C=(pi r^2)/2
C=(400pi)/2
C=200pi
So the shaded area is
A=2600-200pi
A=1972 (rounded to nearest 1)
Walt's Marina generated the following regression based on the number and cost of daily rentals of its boat slips to boat owners each month.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.425358
R Square 0.481216
Adj RSquare 0.456695
Stand. Error 39.35892
Observations
ANOVA Sig
df SS MS F sig F
Regression 1 43,034.7 43,034.71 0.000151
Residual 13 20,138.6 1,549.12
Total 14 63,173.3
MS Full 27.780017 | 14 Intercept X Variable 1
Coefficients Std Error t Stat P-value Lower Upper Lower Upper
95% 95% 95% 95%
Intercept 2621.21101.8073 2.626725 0.020917 47.478460 487.3612 47.478460 X variable 35.58 6.1023 5.270675 0.000151 18.980154 45.3467 18.980154
Walt's Marina rents 45 boat slips each month (within relevant range), how much is its total cost for boat slip rentals?
A. $4,222
B. $8,722
C. $4,581
D. Not available based on the information
Which one of the following is a purely fixed cost?
1000 units 2000 units
Total Per Unit Total Per Unit
Cost A 500 0.2 1000 0.2
Cost B 2000 5 2000 2.5
Cost C 750 3.2 1000 2.4
Cost D 100 0.5 250 0.3
A. Cost A
B. Cost B
C. Cost C
D. Cost D
Answer:
The answer is "Option A and Option B"
Step-by-step explanation:
In question 1:
The fixed cost=2621.21
The unit variable cost=35.58
Calculating the total cost for 45 boat slips:
[tex]=2621.21+(45 \times 35.58)\\\\=2621.21+(1601.1)\\\\=4222.31 \approx 4222[/tex]
In question 2:
It is the pure fixed costs that remain consistent in total regardless of dynamic loads. An overall cost B both for 1000 and 2000 unit is unchanged, therefore the Cost B is a fixed sum.
At the movies, tickets cost $12 for adults and $6.50 for kids under 12.
How many total tickets would someone get if they purchased 7 adult
tickets and 9 kids tickets? How many total tickets would someone get if
they purchased a adult tickets and k kids tickets?
Answer:
104 in total
6.5k+12a=18.5ka
Step-by-step explanation:
Can someone explain how to do this for me!
Answer:
x = 90 degrees
Step-by-step explanation:
the above figure is of a circle, so the sum of the measures of angles will be 360 degrees.
measure of arc = measure of the angle inscribed by the arc
therefore, the measure of arc JK will also be x...... ( vertically opposite angles)
therefore, x + x + 30 + (2x - 30) = 360 .....(1)
therefore, 2x + 30 + 2x - 30 = 360
therefore, 4x = 360.....( as -30 and +30 will be cancelled)
therefore, x = 90 degrees
Cross correction:-
by putting in x = 90 in (1)
90 + 90 + 30 + 2*90 - 30 = 360
180 + 30 + 180 - 30 = 360
180 + 180 = 360
so, x= 90 degrees is verified.
Need ASAP
What is the measure of angle m in kite klmn
g(x)=3x-2
FIND g(8)
Please helpppppppppppp
Answer:
g(8) = 3(8)-2
g(8) = 24-2
g(8)= 22
Step-by-step explanation:
— 5 3/4 - 3 1/2
I need help fast
Answer:
-9 1/4
Step-by-step explanation:
Answer:
i also need help
Step-by-step explanation:
do it yourself
PLEASE SOLVE THIS FOR ME ITS MY MIDTERM
your class earned 90.00 saturday afternoon by washing cars to raise money for a class trip this is 1/6 of money needed for trip what is the total amount needed
Answer:
540
Step-by-step explanation:
We need 6 times 90 for the full amount.
Answer:
Total amount = 540
Step-by-step explanation:
let total amount = x
1/6 * x = 90
x = 540
A recipe for potato casserole calls for 7/4 cups of cheese. Write the fractions as a mixed number.
Alina's home is 15km from Sentosa. She cycles a distance of 8km. What percentage of the total distance does she have left to cover? Give your answer correct to 2 decimal places.
Answer:
55.5 percent of the way!!!!!!
what is the slope if it goes through (0, 2) and (-2, 3)
Complete the table values for y=3x-4
Pleas help
Step-by-step explanation:
(-1,-7) (0,-4) (1,-1) (2,2) (3,5) (4,8)
if you have any questions about this, don't hesitate to ask :))
if f(x)=x^2 domain=[-1,2], the range is ?
Write an equation in slope-intercept form for the line with slope -3/4 and y-intercept for 3
Answer:
y=-3/4x+3
Step-by-step explanation:
The formula is y=mx+b
m is the slope
b is the y-intercept
If you plug it in, you get y=-3/4x+3
Hope this helps!
Use a linear approximation (or differentials) to estimate the given number. (Round your answer to two decimal places.) (1.999)3
Consider the function f(x) = x ³. Since 2³ = 8 is a perfect cube that is pretty close to x = 1.999, take the linear approximation to f(x) at x = 2. It is
f(x) ≈ L(x) = f (2) + f ' (2) (x - 2)
Compute the derivative:
f(x) = x ³ → f ' (x) = 3x ² → f ' (2) = 12
Then
L(x) = 8 + 12 (x - 2) = 12x - 16
Now approximate 1.999³ :
f (1.999) ≈ L (1.999) = 12•1.999 - 16 = 7.988
(Compare this to the actual value, 7.98801.)
What is the recursive formula for this arithmetic sequence?
-7, -1, 5, 11, ...
Answer:
The answer is A
Step-by-step explanation:
why it is a is...
the first like is the # your arithmetic sentence starts with which is -1
the second line is what you do to get to the next #
each time you are adding 6
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The correct option is A.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
[tex]a_n = a_1 + (n-1)d[/tex]
Also, the recursive formula for any arithmetic series is given by the formula,
[tex]a_n = a_{(n-1)} + d\\\\[/tex]
Or, it can be also written as,
[tex]a_{(n+1)} = a_{n} + d[/tex]
where d is the difference and a₁ is the first term of the sequence.
For the given arithmetic sequence, the common difference can be written as,
Common difference = -1 - (-7)
= -1 + 7
= 6
Now, the recursive formula for this arithmetic sequence can be written as,
[tex]a_n = a_{(n-1)} + 6[/tex]
Also, the first term of the given arithmetic series is -7.
a₁ = -7
Hence, the correct option is A.
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Ensuring that there are NO Parenthesis or other groupings and NO Like Terms represents the process for _____________________.
A, simplifying an expression.
B,using substitution to solve an expression.
C,converting a fraction to a decimal.
D,comparing rational numbers.
What is the surface area of the rectangular prism?
16 cm 2
48 cm 2
96 cm 2
80 cm 2
Answer:
Surface area = 80 cm²
Step-by-step explanation:
Surface Area of rectangular prism = 2(LW + LH + WH)
L = 4 cm
W = 4 cm
H = 3 cm
Plug in the values
Surface Area = 2(4*4 + 4*3 + 4*3) = 2(16 + 12 + 12)
Surface Area = 2(40) = 80 cm²
[tex]4x - {x}^{3} [/tex]
2/3 divided by 5
Send help for me please
Answer: 0.13
Step-by-step explanation:
The sixth grade class is going to the local art musem's dinoaurexhibit. There was 52 students in the class. The total cost of the tickets for all the students is $364. What is the cost of one student ticket?
8/9+8/9
enter answer as a fraction