Answered: m&m's are packaged by weight, rather…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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m&m's are packaged by weight, rather than by number of pieces, but consumers expect to have about 50 peices of candy in a single serving size bag. The number of pieces in a bag is normally distributed with a mean of 52.4 and a standard deviation of 2.2.

a. Find the z-score corresponding to a bag with 47 pieces. Round your answer to 2 decimal places.

b. Find the probability of a bag containing 47 or fewer pieces. Round your answer to 4 decimal places.

c. A customer will be dissatisfied if they purchase a bag that contains fewer than 47 pieces. What percentage of customers will be dissatisfied? Round your answer to 2 decimal places.

The machine that packages the m&m's can be reset to change the average number per bag, although the variability (the standard deviation) will remain the same. What should the average be set to, in order to ensure that fewer than 1% of customers are dissatisfied with their purchase? Round your answer to 1 decimal place.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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