Answer:
0.9803 = 98.03% probability that not more than 650 parents will attend the graduation ceremony.
Step-by-step explanation:
To solve this question, we need to know the Poisson and the normal distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval. The standard deviation is the square root of the mean.
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.
The Poisson distribution can be approximated to the normal with same means, and [tex]\sigma = \sqrt{\mu}[/tex]
1/3 of the graduating seniors at a certain college have two parents attend the graduation ceremony, another third of these seniors have one parent attend the ceremony, and the remaining third of these seniors have no parents attend.
There are 600 graduating seniors. This means that the expected number of parents attending the ceremony is given by:
[tex]\mu = 600*(2*\frac{1}{3} + 1*\frac{1}{3} + 0*\frac{1}{3}) = 600(\frac{2}{3} + \frac{1}{3}) = 600(1) = 600[/tex]
And
[tex]\sigma = \sqrt{600}[/tex]
What is the probability that not more than 650 parents will attend the graduation ceremony?
Using continuity correction, as Poisson is a discrete distribution while the normal is continuous, this is [tex]P(X \leq 650 + 0.5) = P(X \leq 650.5)[/tex], which is the pvalue of Z when [tex]X = 650.5[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{650.5 - 600}{\sqrt{600}}[/tex]
[tex]Z = 2.06[/tex]
[tex]Z = 2.06[/tex] has a pvalue of 0.9803.
0.9803 = 98.03% probability that not more than 650 parents will attend the graduation ceremony.
The measure of an angle is 72 degrees what is the measure of its conplementary angle
Answer:
18
Step-by-step explanation:
what is the remainder
The first week of January it
snowed 12 inches. This week
it snowed 16 inches. How
many inches has it snowed in
all?
Answer:
28 inches
Step-by-step explanation:
the answer is 28 inches
12+16= 28
Number of snow snowed in January = 12 inches
Number of snow snowed this week = 16 inches
Number of snow snowed at all = 12+16
= 28 inches
hence it snowed 28 inches at all
PLEASE I NEED HELP THIS NEEDS TO GET DONE SOON AND IM STUCK):
Question 2 Multiple Choice Worth 2 points) (06.03) For the expression y + 6 - 3, determine the coefficient for the variable term 1 06
Answer:
1
Step-by-step explanation:
whenever there is a varible alone the coefficient is 1
Mickey’s Pizza charges $5 per Medium Pizza and a $4 delivery charge.
Make a table with the following information:
Pizzas: 1, 2, 3, 4, 5
Cost:
Equation:
6t/9-22;t=60
please help me
Answer:
if t=60, then 6(60)/9-23. (360-198)/9
=18
Can someone help me it’s due tomorrowwwww
Number one is straight angle
number two is obtuse
number three is acute
Number 4 is acute
number 5 is a right angle
number 6 is obtuse
number 7 is right angle
number 8 is obtuse
If M= {m, a,t} how many subsets of M are there?
Answer:
8 {m},{a},{t},{m,a},{m,t},{a,t},{m,a,t},{}
5. X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. This can be written as N(8,4). The probability that X is between 1.48 and 15.56 is _____________. Write out the probability notation for this question.
Answer:
The probability that X is between 1.48 and 15.56 is [tex]P(1.48 \leq X \leq 15.56) = 0.919[/tex]
Step-by-step explanation:
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.
X is a normally distributed random variable with a mean of 8 and a standard deviation of 4.
This means that [tex]\mu = 8, \sigma = 4[/tex]
The probability that X is between 1.48 and 15.56
This is the pvalue of Z when X = 15.56 subtracted by the pvalue of Z when X = 1.48. So
X = 15.56
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15.56 - 8}{4}[/tex]
[tex]Z = 1.89[/tex]
[tex]Z = 1.89[/tex] has a pvalue of 0.9706
X = 1.48
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.48 - 8}{4}[/tex]
[tex]Z = -1.63[/tex]
[tex]Z = -1.63[/tex] has a pvalue of 0.0516
0.9706 - 0.0516 = 0.919
Write out the probability notation for this question.
[tex]P(1.48 \leq X \leq 15.56) = 0.919[/tex]
The probability that X is between 1.48 and 15.56 is [tex]P(1.48 \leq X \leq 15.56) = 0.919[/tex]
ill mark brainlist plss help
Answer:
C. 99 yd^2
Step-by-step explanation:
The formula for solving for area of a triangle is 1/2*b*h.
18*11=198
198/2=99
Can somebody help me?
Answer:smsjsjsjsjsjss
Step-by-step explanation:idididididisjsnsbuxxjhx
Ssjsjsjsjjssjsjmsjsjsjs
The approximate length (in cm) of a typical Pacific halibut t years old is given by f(t) = 200(1 -0.956e-0.181).
A Pacific lialibut caught by Mike measures 140cm. What is its approximate age?
Answer:
6 years old
Step-by-step explanation:
Given
[tex]f(t) = 200(1 -0.956e^{-0.18t})[/tex]
Required
Find t when f(t) = 140cm
Substitute f(t) = 140cm
[tex]140 = 200(1 -0.956e^{-0.18t})[/tex]
Divide both sides by 200
[tex]0.7 = 1 -0.956e^{-0.18t}[/tex]
Collect like terms
[tex]0.956e^{-0.18t} = 1 -0.7[/tex]
[tex]0.956e^{-0.18t} = 0.3[/tex]
Solve for t
[tex]e^{-0.18t} = 0.3/0.956[/tex]
[tex]e^{-0.18t} = 0.31381[/tex]
Take natural logarithm of both sides
[tex]ln(e^{-0.18t}) = ln(0.31381)[/tex]
[tex]-0.18tln(e) = ln(0.31381)[/tex]
[tex]-0.18t*1 = ln(0.31381)[/tex]
[tex]-0.18t = -1.159[/tex]
Solve for t
[tex]t = (-1.159)/(-0.18)[/tex]
[tex]t = 6.43[/tex]
[tex]t \approx 6[/tex]
What is equivalent to -8z+ (-3.5) +1.5z+3y-5.5
Answer: =3y−6.5z−9
Step-by-step explanation:
Does someone know the answer I NEED IT NOW
Answer:
2nd option ,
A is correct, B is incorrect, C is correct
Explain how to use the Pythagorean Theorem to find the missing length of a right triangle.
Pythagorean theorem.
a^2+b^2=c^2
This means that the square of the length of the 2 legs of a right triangle added together = the square of the length of the hypotenuses or diagonal.
If you know 2 of the values in the 3 variables a,b,c what would you do to find the missing variable value?
I will not write the exact answers to this problem. I think you can figure how to write it out yourselves.
How many thirds are in 12?
Find the values of x and y.
x+x+90=180
x+x+90=1802x+90=180
x+x+90=1802x+90=1802x=180-90
x+x+90=1802x+90=1802x=180-902x=90
x+x+90=1802x+90=1802x=180-902x=902x/2x =90/2
x=45
9y+9y+90=180
18y+90=180
18y=180-90
18y=90
18y/18 =90/18
y=5
Accuracy in taking orders at a drive-through window is important for fast-food chains. Periodically, QSR Magazine publishes "The Drive-Thru Performance Study: Order Accuracy" that measures the percentage of orders that are filled correctly. In a recent month, the percentage of orders filled correctly at Burger King was approximately 90.5%. Suppose that you and two friends go to the drive-through window at Burger King and place an order. Two friends of yours independently place orders at the window at the same store.
a. What is the probability that all the three orders will be filled correctly?
b. What is the probability that none of the three will be filled correctly?
c. What is the probability that one of the three will be filled correctly?
d. What is the probability that at least one of the three will be filled correctly?
e. What is the probability that only your order will be filled correctly?
Answer:
a) 0.7412 = 74.12% probability that all the three orders will be filled correctly.
b) 0.0009 = 0.09% probability that none of the three will be filled correctly
c) 0.0245 = 2.45% probability that at least one of the three will be filled correctly.
d) 0.9991 = 99.91% probability that at least one of the three will be filled correctly
e) 0.0082 = 0.82% probability that only your order will be filled correctly
Step-by-step explanation:
For each order, there are only two possible outcomes. Either it is filled correctly, or it is not. Orders are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The percentage of orders filled correctly at Burger King was approximately 90.5%.
This means that [tex]p = 0.905[/tex]
You and 2 friends:
So 3 people in total, which means that [tex]n = 3[/tex]
a. What is the probability that all the three orders will be filled correctly?
This is P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.905)^{3}.(0.095)^{0} = 0.7412[/tex]
0.7412 = 74.12% probability that all the three orders will be filled correctly.
b. What is the probability that none of the three will be filled correctly?
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.905)^{0}.(0.095)^{3} = 0.0009[/tex]
0.0009 = 0.09% probability that none of the three will be filled correctly.
c. What is the probability that one of the three will be filled correctly?
This is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.905)^{1}.(0.095)^{2} = 0.0245[/tex]
0.0245 = 2.45% probability that at least one of the three will be filled correctly.
d. What is the probability that at least one of the three will be filled correctly?
This is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
With what we found in b:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0009 = 0.9991[/tex]
0.9991 = 99.91% probability that at least one of the three will be filled correctly.
e. What is the probability that only your order will be filled correctly?
Yours correctly with 90.5% probability, the other 2 wrong, each with 9.5% probability. So
[tex]p = 0.905*0.095*0.095 = 0.0082[/tex]
0.0082 = 0.82% probability that only your order will be filled correctly
How do you check your answer or plug it in after solving |2x + 1| = 9 ???
Step-by-step explanation:
2x + 1 = 9
2x = 9 - 1
2x = 8
x = 8 ÷ 2
x = 4
----------------------------------FOLLOW MEPLEASE
Answer:
Step-by-step explanation:
To solve:
|2x+1|=9
|2x+1|=-9
2x=8
x=4
2x=-10
x=-5
2x+1=9
2(4)+1=9
9=9, so its true.
2x+1=-9
2(-5)+1=-9
-9=-9, so it’s true too
In the first 15 seconds of the rollercoaster, passengers are carried up a 90-meter hill, plunged down 62 meters, and quickly taken back up a 38-meter rise. How much higher or lower from the start of the ride are they after these 15 seconds?
Answer:
90-62=28
28+38=66
90-66=24
in 15 seconds they are 24 meters lower
A suitcase is discounted 40 % off the original price, p . Which expression represents the price of the suitcase with the discount?
Answer:
Step-by-step explanation:
b
0.6p is the expression represents the price of the suitcase with the discount
How to calculate perecent discountHow can I figure out a discount of X%?You apply the fundamental formula given above in this situation.Take the original cost.The result is multiplied by the discount and divided by 100.Subtract the updated amount from the starting cost.Your total price is that. Enjoy your discounts!To learn more about discount, refer to https://brainly.com/question/1548141
#SPJ1
what is the value of p+9 when p=16
Answer:
25 :)
Step-by-step explanation:
well, if it's p+9 and you know that p=16 then you plug 16 in for p so the equation will be 16+9 and then you solve from there which is 25
Expand t (4t - 4 ) answer if you can plz
Answer:
42−4
Step-by-step explanation:
Answer:
4t^2 −4t
Step-by-step explanation:
t(4t−4)
Use the distributive property to multiply t by 4t−4.
4t^2 −4t
What is 75% of 162? Show your work and/or explain your reasoning.
Answer:
121.5
Step-by-step explanation:
75% = 75/100
Step 2 - Mutiply percenatge fraction by the entire (100%) quantity
75/100× 162 = 121.5
Final result
75 percent of 162 is 121.5
Answer:
121.5
Step-by-step explanation:
| percantage x 100% |
75/100 x 162 = 121.5
Can somebody help and show work
Answer:
( x +1 ) ( x + 3 )
There were 45 runners to start a race. In the first half of the race, 2/3
of them dropped out. In the second half of the race, 4/5
of the remaining runners dropped out. How many runners finished the race?
runners?
Answer:43 8/15
Step-by-step explanation:45-2/3 is 44 1/5 then subtract 44 8/15 by 4/5 and you get 43 8/15
Mr. Taylor has 24 sports trophies. Of the trophies, 1
8 are wrestling trophies. How many
wrestling trophies does Mr. Taylor have?
Answer: 18 wrestling trophies.
Step-by-step explanation:
Notice that the rule for each animal involves counting the number of chirps in different time intervals. For the Brookdale cricket you count the number of chirps in 15 seconds and for the katydid you count the number of chirps in 20 seconds. If c is the number of chirps per minute, what is the expression for the number of chirps for i) The Brookdale cricket in 15 seconds
3/4 of 1/3 =? please show me how to do it
Can someone help with this asap ?
Answer:
y=-(x+11)(x-23)
Step-by-step explanation:
y=-(x+11)(x-23)
use the x intercepts they give you, and make it the opposite i.e. if it positive, then make it negative if it is negative make it positive
i.e. -11 equals 11
thus (x+11)
then, the graph is concave down, so it is negative at the front