Question

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 66.8 grams and a standard deviation of 1.94 grams.

a) For samples of size 16 pizza slices, what is the standard deviation for the sampling distribution of the sample mean?

b) What is the probability of finding a random slice of pizza with a mass of less than 66.3 grams?

c) What is the probability of finding a 16 random slices of pizza with a mean mass of less than 66.3 grams?

d) What sample mean (for a sample of size 16) would represent the bottom 15% (the 15th percentile)?  grams

Answer 1

Solution :

Given that ,

mean = = 66.8

standard deviation = = 1.94

n = 16

= 66.8

standard deviation for the sampling distribution of the sample mean

=  / n = 1.94 / 16=0.485

b.

P(X<66.3 ) = P[(X- ) / < (66.3-66.8) / 1.94]

= P(z <-0.26 )

Using z table

= 0.3974

c.

P( <66.3 ) = P[( - ) / < (66.3-66.8) / 0.485]

= P(z <-1.03 )

Using z table

= 0.1515

d.

Using standard normal table,

P(Z < z) = 15%

= P(Z < z) = 0.15

= P(Z < z ) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < z ) = 0.85  

z = 1.04

Using z-score formula  

= z * +

= 1.04 *0.485+66.8

= 67