Power Inc. produces remote-controlled toy cars. The mean life of these batteries

Question

Power Inc. produces remote-controlled toy cars. The mean life of these batteries hours. the normal probability distribution with hours. hours and a standard deviation of 5.8 As a part of its quality assurance program, Power Inc. tests samples of batteries. a. What can you say about the shape of the distribution of the sample mean? Sample mean Normal b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.) Standard error 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 d. What proportion of the sam 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 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 Probability

Explanation / Answer

a) Mean lif eof batteries follow a normal distribution, shape of distribution of sample mean is normal.

b) Standard derror=s/srt n=5.8/sqrt 9=1.9333

c) Compute z score and find corresponding area to obtain the require proportion.

z=(Xi-Xbar)/s=(39.5-38)/5.8=0.26, the proportion of sample is 0.1026.

d) z=(37.5-38)/5.8=-0.09. The proportion of sample is 0.4641.

e) Required proportion is (0.1026+0.4641)=0.5667.

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