In: Math
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 5.8 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries. |
( I specifically would like to know how to get z step by step for C and D)
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 39.5 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 37.5 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 37.5 and 39.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) |
Probability |
|
(a) The distribution of sample means is Normal Distribution.
(b) SE = /
= 5.8/= 1.9333
(c) To find P( > 39.5):
Z = ( - )/SE
= (39.5 - 38)/1.9333 = 0.78
Table of Area Under Standard Normal Curve gives area = 0.2823
So,
P(>39.5) =0.5 - 0.2823 = 0.2177
(d)
To find P( > 37.5):
Z = ( - )/SE
= (37.5 - 38)/1.9333 = - 0.26
Table of Area Under Standard Normal Curve gives area = 0.1026
So,
P(>39.5) =0.5 + 0.1026 = 0.6026
(e)
To find P(37.5 < <39.5):
Case 1: For from 37.5 to mid value:
Z = ( - )/SE
= (37.5 - 38)/1.9333 = - 0.26
Table of Area Under Standard Normal Curve gives area = 0.1026
Case2 : For from mid value to 39.5:
Z = ( - )/SE
= (39.5 - 38)/1.9333 = 0.78
Table of Area Under Standard Normal Curve gives area = 0.2823
P(37.5 < < 39.5) =0.1026 + 0.2823 = 0.3849