Power Inc. produces AA batteries used in remote-controlled toy cars. The mean li

Question

Power Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 38 hours. hours and a standard deviation of 5.8 hours. As a part of its quality assurance program, Power+,Inc. tests samples of 9 batteries. a. What can you say about the shape of the distribution of the sample mean? Sample mean Normal b. at is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.) Standard error 1.9333 c. What proportion of the samples will have a mean useful life of more than 39.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability 0.1026 d. What proportion of the sample will have a mean useful life greater than 37.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability 0.4641 o e. What proportion of the sample will have a mean useful life between 37.5 and 39.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) o 0.5667 Probability

Explanation / Answer

c) Xi=39.5, Xbar=38, s=5.8/sqrt 9=1.93

z=(Xi-Xbar)/s=(39.5-38)/1.93

=0.78

Required proportion:0.2823

d) z=(37.5-38)/1.93=-0.26

Required proportion is 0.3974

e) Required proportion: (0.2823+0.3974)=0.6797

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