A certain coffee shop sells coffee and doughnuts. The owner believes that the nu

Question

A certain coffee shop sells coffee and doughnuts. The owner believes that the number of cups he sells each day is normally distributed with a mean of 150 cups and standard deviation of 12 cups. He also thinks that the number of doughnuts sold each day is normally distributed with a mean of 135 doughnuts and standard deviation of 9. Assume independence.

If the shop is open 7 day in a week, what is the probability of selling an average of 155 cups of coffee in a week?

a) 0.8473

b) 0.4729

c) 0.1351

d) 0.0053

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean of the sampling distribution ( x ) = 150
standard Deviation ( sd )= 12/ Sqrt ( 7 ) =4.5356
sample size (n) = 7
P(X > 155) = (155-150)/12/ Sqrt ( 7 )
= 5/4.536= 1.1024
= P ( Z >1.1024) From Standard Normal Table
= 0.1351

c) 0.1351

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