Question

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.8 grams and a standard deviation of 2.11 grams. Round answers to three decimal places. a) For samples of size 22 pizza slices, what is the standard deviation for the sampling distribution of the sample mean? Incorrect b) What is the probability of finding a random slice of pizza with a mass of less than 67.1 grams? Incorrect c) What is the probability of finding a 22 random slices of pizza with a mean mass of less than 67.1 grams? Incorrect d) What sample mean (for a sample of size 22) would represent the bottom 15% (the 15th percentile)? Incorrect grams

Answer 1

a) = = 2.11/ = 0.450

b) P(X < 67.1)

= P((X - )/ < (67.1 - )/)

= P(Z < (67.1 - 67.8)/2.11)

= P(Z < -0.33)

= 0.3707 = 0.371

c) P( < 67.1)

= P(( - )/() < (67.1 - )/())

= P(Z < (67.1 - 67.8)/(2.11/))

= P(Z < -1.56)

= 0.0594 = 0.059

d) P( < x) = 0.15

Or, P(( - )/() < (x - )/()) = 0.15

Or, P(Z < (x - 67.8)/(2.11/)) = 0.15

Or, (x - 67.8)/(2.11/) = -1.04

Or, x = -1.04 * (2.11/) + 67.8

Or, x = 67.332