Answered: The depletion time of a vital resource…

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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Question

The depletion time of a vital resource in a production process is believed to be normally distributed with a mean of μ=40minutes and a standard deviation of σ=2.4 minutes. A recently appointed production team introduced new efficiencies that they claim make the depletion of the resource slower. To test this claim, a random sample of n=12 production shifts were taken and the observed mean depletion time of the resource was x¯=40.5 minutes

a. In testing the production team's claim, select the appropriate alternative hypothesis, H1 or Ha:

μ≠40.5

μ<40.5

μ>40.5

μ≠40

μ<40

μ>40

b. At α=0.015, determine the critical value:

Round to two decimal places

c. The value of the test statistic:

Round to two decimal places

d. At α=0.015,, select the decision / conclusion:

sufficient evidence to conclude that the new efficiencies introduced make the depletion of the resource slower.

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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