00:01
A car company is found that the lifetime of its batteries varies from car to car according to a normal distribution with mu equals 48 months in standard deviation, sigma equals 8 .2 months.
00:18
The company installs a new brand of battery on a simple random sample of eight cars.
00:23
That's the sample size.
00:27
If the new brand has the same lifetime distribution as the previous type of battery, describe the sampling distribution of the mean lifetime x bar.
00:37
Well, this is going to be normal because the population.
00:39
Has a normal distribution.
00:42
So the mean of the sampling distribution would be equal to the population mean which is 48 months and the standard deviation of the sampling distribution would be sigma divided by the square root of n.
01:09
So that's going to be the 8 .2 divided by the square root of 8 which is about 2 .891 months for part b, the average life of the batteries on these eight cars turns out to be 42 .2 months...