Question

An electrical firm manufacturers batteries that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 64 batteries has an average life of 780 hours, find the bounds of a 95% confidence interval for the population mean of all batteries produced by this firm.

Answer 1

The values provided in the above question are as below

Sample mean = = 780

standard deviation = = 40

Sample size = = 64

Confidence level = 95% = 0.95

1 - = 0.95

= 1 - 0.95

= 0.05

/2 = 0.025

We find is the z-value leaving an area of 0.025 to the right.

That is, the probability of this area is 1 - 0.025 = 0.975

Using standard normal table

We find the z value whose probaility is 0.975 that is 0.9750 (Using 4 decimal places)

Because, all the probability values in standard normal table are in 4 decimal places.

We find the bounds of a 95% confidence interval for the population mean of all batteries produced by this firm using following formula

Or

The bounds of a 95% confidence interval for the population mean of all batteries produced by this

firm are (770.2, 789.8)

Summary :-

The bounds of a 95% confidence interval for the population mean of all batteries produced by this

firm are (770.2, 789.8)