SOLUTION: Checkout times in a Wal-Mart store follow a normal distribution with a mean time of 8 minutes and standard deviation of 1.5 minutes.
a. What is the probability that the checkout
Algebra.Com
Question 670561: Checkout times in a Wal-Mart store follow a normal distribution with a mean time of 8 minutes and standard deviation of 1.5 minutes.
a. What is the probability that the checkout time for the next customer will be 6 minutes or less?
b. 80% of the customers need more than C minutes to checkout. Calculate C.
A sample of 40 clients is selected randomly.
c. What is the probability distribution of the sample mean? Explain.
d. What is the probability that the mean of the sample is between 6 and 7 minutes?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Checkout times in a Wal-Mart store follow a normal distribution with a mean time of 8 minutes and standard deviation of 1.5 minutes.
---
For each of these problems you have to convert the raw numbers to z-numbers,
then look up the probability on a z-chart or use a calculator.
-----
a. What is the probability that the checkout time for the next customer will be 6 minutes or less?
z(6) = (6-8)/1.5 = -2/1.5 = -4/3
P(x <=6) = P(z <= -4/3) = normalcdf(-100,-4/3) = 0.0912
=============================================================
b. 80% of the customers need more than C minutes to checkout. Calculate C.
A sample of 40 clients is selected randomly.
c. What is the probability distribution of the sample mean? Explain.
mean of sample means = 8
std of sample means = 1.5/sqrt(40)
Stated in The Central Limit Theorem
--------------------------------------------
d. What is the probability that the mean of the sample is between 6 and 7 minutes?
z(6) = (6-8)/[1.5/sqrt(40)) = -8.4327
z(7) = (7-8)/(1.5/sqrt(40)) = -4.2164
---
P(6 <= x <= 7) = P(-8.4327 <= z <= -4.2164) = normalcdf(-8.4327,-4.2164)
= 0.00001242
====================
Cheers,
Stan H.
RELATED QUESTIONS
1. In a survey, 1,000 kids were asked if they owned a pair of tennis shoes and if they... (answered by solver91311)
Jim’s Auto Insurance Company customers sometimes have to wait a long time to speak to a (answered by math_tutor2020)
The heights of children aged between 8 and 15 follow a normal distribution with mean of... (answered by ikleyn)
Two machines M1, M2 are used to manufacture resistors with a design
specification of... (answered by Boreal)
The length of time a customer must wait in line at the post office has approximately a... (answered by stanbon)
the length of time a customer must wait in line at the post office has approximately a... (answered by stanbon)
The one way commute time is 25.8 minutes. The longest one way travel time is in New York... (answered by amarjeeth123)
The weights of trout in a certain river follow a normal distribution with mean 3 pounds... (answered by stanbon)
Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a... (answered by stanbon)