Question

Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows a normal distribution with a mean of 37 hours and a standard deviation of 5.6 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 16 batteries.

  

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

   

Sammple mean

normal (already have this answered)

Round answers to four decimal places.

b.	What is the standard error of the distribution of the sample mean? Note: The standard error is the standard deviation of the distribution of the sample mean. That is, the standard error is the population standard deviation divided by the square root of the sample size.

   

Standard error

c.	What proportion of the samples will have a mean useful life of more than 38 hours?

   

Probability

d.	What is the probability that a randomly selected AA battery will have a useful life of at most 36 hours?

   

Probability

e.	What proportion of the samples will have a mean useful life between 36 and 38 hours?

   

Probability

Answer 1

b)

mean μ= 37 hours

standard deviation s = 5.6

sample n =16

standard error of the distribution = s / √n = 5.6 /√16 = 5.6 /4 = 1.4

c)

proportion of the samples more than 38

P( X > 38) =  x - μ/ σ / √n

= 38 - 37 / 5.6 / √16

. = 1 / 1.4

= 0.7143

P ( Z > 0.7143) = 1−P ( Z<0.7143 )=1−0.7611=0.2389

d)

proportion of the samples atmost 36

P( X < 36) =  x - μ/ σ / √n

= 36 - 37 / 5.6 / √16

. = -1 / 1.4

= -0.7143

P ( Z < -0.7143) = 1−P ( Z<0.7143 )=1−0.7611=0.2389

e) proportion of the samples  between 36 and 38 hours

P ( 36 <X < 38) = P( 36 - 37 / 5.6 / √16 < Z < 38 - 37 / 5.6 / √16 )

= P( - 0.7143 < Z < 0.7143 )

P( - 0.7143 < Z < 0.7143 ) =0.5222