Power Inc produces AA batteries used in remotecontrolled toy

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 35 hours and a standard deviation of 5.2 hours. As a part of its quality assurance program, Power+, Inc. tests samples of 9 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 36 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 34 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 34 and 36 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

Solution

a) Normal
b)
Standard Error= sd/ Sqrt(n)
Where,
    sd   = Standard Deviation
    n = Sample Size

Standard deviation( sd )=5.2
Sample Size(n)=9
Standard Error = ( 5.2/ Sqrt ( 9) )
= 1.733
c)
P(X > 36) = (36-35)/5.2
= 1/5.2 = 0.1923
= P ( Z >0.192) From Standard Normal Table
= 0.4238 = 42.38%                  
d)
P(X > 34) = (34-35)/5.2
= -1/5.2 = -0.1923
= P ( Z >-0.192) From Standard Normal Table
= 0.5762 = 57.62%              
e)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 34) = (34-35)/5.2
= -1/5.2 = -0.1923
= P ( Z <-0.1923) From Standard Normal Table
= 0.42375
P(X < 36) = (36-35)/5.2
= 1/5.2 = 0.1923
= P ( Z <0.1923) From Standard Normal Table
= 0.57625
P(34 < X < 36) = 0.57625-0.42375 = 0.1525 = 15.25%