00:01
To solve these problems we'll use the properties of the normal distribution.
00:04
Given that the population has a normal distribution with a mean of 226 .7 and a standard deviation of 89 .1, then the probability that we have a single value from the sample that it falls between 214 .7 and 232 .7, we need to standardize these values using a z -score.
00:33
And so for the lower limit would be 214 .7 minus the mean over the standard deviation.
00:43
And for our second score would be 232 .7 for the upper limit.
00:58
And we throw these into a calculator.
01:01
We get negative 0 .1347 and 0 .0673.
01:32
And then we need to find the area under the standard normal curve between these z -scores using a standard normal distribution table or a calculator.
01:40
I'll put it into a calculator.
01:47
So this will be equal to the probability that z is in between these two values, which i'll go to four decimal places as well.
02:05
And you get 0 .0804...