00:01
So our questions is data on the basal body temperature of sample of 65 women review the mean to be 98 .4 degrees fahrenheit and the standard division of 0 .7 4 degree fahrenheit.
00:12
Suppose these values accurately estimate the true population mean and the standard division of the body temperature among all women.
00:20
And suppose that the body temperature are normally distributed.
00:23
What is the proportion of women have? what proportion of women have a basal body temperature above 97 .3 degree ferriads.
00:32
And the second question says, what proportion of women have a basal body temperature between 97 .1 and 98 .9 degrees farriats? and the third question says, at what body temperature rounded to the nearest 100 of degree is the 85th percentile of the distribution? so let's go into our worksheet and extract out all of our necessary details.
00:55
We have the sample size n to be equals to 65.
00:58
5 we have the population mean m to be equals to 98 .4 and we have the population standard difference equals to 0 .74 so the first question says what proportion of women have a basal body temperature above 97 .3 so the first question is probability that x is greater than 97 .3 so to get this probabilistic value we have to standardize it that is we have to move from the x call which is the random variable to a z score and to do so we have a formula that z is equal to x minus mu divided by sigma x in this case is 97 .3 minus we have our 98 .4 divided by we have our zigma to be 0 .74 so when we do the math we have minus 1 .1 divided by 0 .74 minus 1 .1 divided by 0 .74 minus 1 .1 divided by 0 .74 and that gives us minus 1 .49.
02:10
So the probability, let's just write it somewhere here, probability that x is greater than 97 .3 is same thing as probability that z is greater than minus 1 .49.
02:22
So i'll be using a calculator to get this.
02:25
So here is my calculator...