Question

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.1 grams and a standard deviation of 2.2 grams. a) For samples of size 12 pizza slices, what is the standard deviation for the sampling distribution of the sample mean? State answer to five decimal places. b) What is the probability of finding a random slice of pizza with a mass of less than 66.5 grams? State the answer to four decimal places. c) What is the probability of finding a 12 random slices of pizza with a mean mass of less than 66.5 grams? State the answer to four decimal places. d) What sample mean (for a sample of size 12) would represent the bottom 15% (the 15th percentile)? State answer to one decimal place. grams

Answer 1

Solution :

Given that ,

mean = = 67.1

standard deviation = = 2.2

n = 12

(a)standard deviation of sampling distribution   = / n = 2.2 / 12 =0.63509

(b)P(x <66.5 ) = P[(x - ) / < (66.5 - 67.1 ) /2.2 ]

= P(z <-0.27 )

Using z table,

=0.3936

(c) n = 12

= 67.1

= / n = 2.2 / 12 =0.6351

P( <66.5 ) = P(( - ) / < (66.5 - 67.1) /0.6351 )

= P(z <-0.95 )

Using z table

= 0.1711

(d) = 67.1

= / n = 2.2 / 12 =0.6351

Using standard normal table,

P(Z < z) =15 %

= P(Z < z) = 0.15

= P(Z <-1.036 ) = 0. 15

z = -1.036

Using z-score formula  

= z * +

= -1.036 *0.6351 + 67.1

= 66.4