Power Inc produces AA batteries used in remotecontrolled to

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 37 hours. hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 25 batteries.  

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

What proportion of the samples will have a mean useful life of more than 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

What proportion of the sample will have a mean useful life greater than 36.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

What proportion of the sample will have a mean useful life between 36.5 and 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

Solution

a.) The sample mean is normal

b.) Standard error = 5.5/25 = 1.1

c.) P(X > 38)

= P( Z > (38 - 37)/1.1)

= P ( Z > 0.91)

= 0.1814

d.) P(X > 36.5)

= P( Z > (36.5 - 37)/1.1)

= P( Z > -0.45)

= 0.6736

e.) P( 36.5 < X < 38)

= P(-0.45 < Z < 0.91)

= P( Z < 0.91) - P(Z < -0.45)

= 0.8186 - 0.3264

= 0.4923