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)

** please hit like, if satisfied from my answer**

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