00:04
To determine the probability that the mean plate thickness of a random sample of 50 metal plates is between 4 .28 and 4 .32 mm, we can use the standard deviation of the population, the sample size, and the given mean.
00:16
The standard deviation of the sample mean, also known as the standard error, can be calculated using the formula standard error is equal to the standard deviation over the square root of the sample size.
00:26
In this case, the standard error is 0 .12 mm over the square root of 50, and that's about 0 .017.
00:45
Next we can calculate the z -scores for the lower and upper bounds of the desired range using the formula z equals the sample mean minus the population mean over the standard error.
00:57
So for the lower bound, that would be 4 .28 minus 4 .3 over 0 .017.
01:13
And for the upper bound, that would be 4 .32 minus 4 .3 over 0 .017.
01:25
And let's calculate that.
01:31
We get negative 1 .18 and positive 1 .1.
01:51
So using a standard distribution table or statistical calculator, we can find the corresponding probabilities associated with these z -scores.
01:58
So probably that the mean plate thickness falls between 4 .28 and 4 .32 is equal to the difference between these probabilities...