5. The weight X, of a widget has the normal distribution with the mean of 50g and standard deviation of 0.8g. (a) Find the probability that a single widget weighs between 49.5 and 50.5g. (b) Find the 85th percentile of the weights. (c) Let be the average weight of 30 widgets. Find the mean and standard deviation of X. Assume that the weights are independent. (d) Approximate the probability that X is between 49.5 and 50.5g. Compare to part (a)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Question
5. The weight X, of a widget has the normal distribution with the mean of
50g and standard deviation of 0.8g.
(a) Find the probability that a single widget weighs between 49.5 and
50.5g.
(b) Find the 85th percentile of the weights.
(c) Let be the average weight of 30 widgets. Find the mean and
standard deviation of X. Assume that the weights are independent.
(d) Approximate the probability that X is between 49.5 and 50.5g.
Compare to part (a)
Transcribed Image Text:5. The weight X, of a widget has the normal distribution with the mean of 50g and standard deviation of 0.8g. (a) Find the probability that a single widget weighs between 49.5 and 50.5g. (b) Find the 85th percentile of the weights. (c) Let be the average weight of 30 widgets. Find the mean and standard deviation of X. Assume that the weights are independent. (d) Approximate the probability that X is between 49.5 and 50.5g. Compare to part (a)
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