Question

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.9 grams and a standard deviation of 2.12 grams. a) For samples of size 18 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 67.1 grams? c) What is the probability of finding 18 random slices of pizza with a mean mass of less than 67.1 grams? d) What sample mean (for a sample of size 18) would represent the bottom 15% (the 15th percentile)?

A. a) 0.5; b) 0.271; c) 0.15; d) 67.5
B. a) 0.47; b) 0.729; c) 0.15; d) 68.1
C. a) 0.47; b) 0.271; c) 0.85; d) 67.5
D. a) 0.47; b) 0.729; c) 0.85; d) 68.1

Answer 1

a) The standard deviation for the sampling distribution of the sample mean is 0.5 grams. b) The probability of finding a random slice of pizza with a mass of less than 67.1 grams cannot be determined without additional information. c) The probability of finding 18 random slices of pizza with a mean mass of less than 67.1 grams cannot be determined without additional information. d) The sample mean that represents the bottom 15% (the 15th percentile) is 67.5 grams.

Step-by-step explanation:

a) For samples of size 18 pizza slices, the standard deviation for the sampling distribution of the sample mean can be found using the formula:

Standard deviation = population standard deviation / square root of sample size

So, in this case, the standard deviation for the sampling distribution of the sample mean is:

Standard deviation = 2.12 grams / square root of 18 = 0.5 grams (approximately)

b) To find the probability of finding a random slice of pizza with a mass of less than 67.1 grams, we need to calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value we're interested in (67.1 grams), μ is the population mean (67.9 grams), and σ is the population standard deviation (2.12 grams).