Question

The lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour. There are nine batteries in a package. What lifetime value (in hours) is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages

Answer 1

The lifetime of the batteries in a package is 14.31 hours which exceeds that value for only 5% of all packages.

Give sample mean of 13 hours and standard deviation of 1 hour and sample size is 9.

We have to apply t test in this because the value of n which is sample size is less than 30.

We have been given the p value of the required mean so we have to find the t value for this with degree of freedom (9-1)=8

t value=2.306.

We know that

t=X bar-μ/s/$\sqrt{n}$

s/$\sqrt{n}$=1/$\sqrt{3}$=0.57

Put all the values in the above formula to calculate required mean.

2.306=X bar-13/0.57

X bar=1.31442+13

=14.31442

after rounding off we get

X bar=14.31

Hence the lifetime of the batteries is 14.31 for which  the percentage exceeds 5%.

Learn more about t test at https://brainly.com/question/6589776

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