Question

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 38 hours. hours and a standard deviation of 5.9 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?

   

Sample mean

(Click to select)NormalUniformBinomial

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 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

   

Probability

d.	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.)

   

Probability

e.	What proportion of the sample will have a mean useful life between 36.5 and 39 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

   

Probability

Answer 1

Solution:

Given that,

mean =   = 38 hours

standard deviation =   = 5 .9 hours

n = 16

a ) The distribution of The sample mean

= 38

B )  The standard error of the distribution of the sample mean

=  ( /n) = (5.9 / 16 ) = 1.4750

Standard error = 1.4750

C ) P (   > 39 )

= 1 - P ( - /) < (39 - 38 / 1.4750)

= 1 -P ( z < 1 / 1.4750 )

= 1 - P ( z < 0.68 )

Using z table

= 1 - 0.7517

= 0.2483

Probability = 0.2483

D ) P (   > 36.5 )

= 1 - P ( - /) < (36.5 - 38 / 1.4750)

= 1 -P ( z < -1.5 / 1.4750 )

= 1 - P ( z < - 1.02 )

Using z table

= 1 - 0.1539

= 0.8461

Probability = 0.8461

E ) P ( 36.5 < < 39 )

P (36.5 - 38 / 1.4750) < ( - /) < (39 - 38 / 1.4750)

P (- 1.5 / 1.4750 < z < 1 / 1.4750 )

P (- 1.02 < z < 0.68 )

P ( z < 0.68 ) - P ( Z < - 1.02 )

Using z table

= 0.7517 - 0.1539

= 0.5978

Probability = 0.5978