Question

Power+, produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 18 hours and a standard deviation of 5.4 hours. As a part of its testing program, Power+ tests samples of 25 batteries. Use Appendix B.1 for the z-values.

a. What can you say about the shape of the distribution of sample mean?

Shape of the distribution is             (Click to select)  Normal  Uniform  Binomial

b. What is the standard error of the distribution of the sample mean? (Round the final answer to 4 decimal places.)

Standard error            

c. What proportion of the samples will have a mean useful life of more than 19 hours? (Round the final answer to 4 decimal places.)

Probability            

d. What proportion of the sample will have a mean useful life greater than 17.5 hours? (Round the final answer to 4 decimal places.)

Probability            

e. What proportion of the sample will have a mean useful life between 17.5 and 19 hours? (Round the final answer to 4 decimal places.)

Probability            

Answer 1

a) Ans - The distribution will be Normal Distribution.

b)

SE = /

= 5.4/ (25)^0.5 = 1.0800 ( rounded to 4 decimal place)

c)  proportion of the samples will have a mean useful life of more than 19 hours is  P( > 19)

Z= (19 - 18)/1.08 = 0.9259

P( > 19) = P(Z > 0.9259) = 1-P(Z < 0.9259 ) = 1- 0.82275

= 0.17725

= 0.1773( rounded to 4 decimal place)

d)

proportion of the sample will have a mean useful life greater than 17.5 hours is P( > 17.5)

Z= (17.5 - 18)/1.08 = -0.46296

P( > 17.5) = P(Z > -0.46296) = 1-P(Z < -0.46296 ) = 1- 0.3217

= 0.6783 ( rounded to 4 decimal place)

e) P(17.5 < X < 19) = P(-0.46296 < Z < 0.9259)

P(Z < 0.9259) - P(Z < -0.46296)

0.82275 - 0.3217

= 0.50105

= 0.5011 ( rounded to 4 decimal place)

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