Vaughn Harper
10/29/2024 · High School
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 2.36 grams. a) For samples of size 22 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 22 random slices of pizza with a mean mass of less than 66.3 grams? d) What sample mean (for a sample of size 22 ) would represent the bottom \( 15 \% \) (the 15 th percentile)?
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a) The standard deviation for the sampling distribution of the sample mean is approximately 0.503 grams.
b) The probability of finding a random slice of pizza with a mass of less than 66.3 grams is approximately 0.367 or 36.7%.
c) The probability of finding 22 random slices of pizza with a mean mass of less than 66.3 grams is approximately 0.057 or 5.7%.
d) The sample mean that would represent the bottom 15% (the 15th percentile) is approximately 66.58 grams.
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