00:01
For this question, we are told that the lengths of pregnancies are normally distributed with a mean of 251 days and a standard deviation of 88 days.
00:10
And for part a, we were asked what proportion of pregnancies last more than 261 days? this is the probability that x is greater than 261.
00:20
If this graph represents the normal distribution of pregnancy length, we have the mean of 251 days exactly in the center.
00:29
Let's say 261 is somewhere around here.
00:32
Probability that x is greater than 261 is equal to the area under the curve and to the right of 261.
00:43
Now since the total area under any probability density curve is 1, this means that the area under the curve to the right of 261 is equal to 1 minus the area under the curve to the left of 261.
00:57
This means that we can re -express this as 1 minus the probability that x is at most 261.
01:05
And now that we have it in terms of accumulative probability, we can solve this using software.
01:10
Such as excel.
01:12
In excel, we start a computation with an equal sign.
01:15
First we have 1 minus, then we want to use the normal distribution function to find the probability that x is anything less than 261.
01:23
We enter 261 for the first argument, then we enter the mean of 251, and the standard deviation of 88, and for the cumulative argument we enter true to get the probability that x is anything less than 261.
01:37
Hit enter, get a probability of 0 .45 -48 approximately.
01:49
And for part b, we want the probability that are randomly selected, or rather we want the proportion of pregnancies that last between 249 and 253 days.
02:00
This proportion is equal to the probability that x is between 249 and 253.
02:11
We want to express this in terms of cumulative probabilities.
02:14
This is equal to the probability that x is less than 253, minus the probability that x is at most to 249.
02:27
So let's go to excel to solve this.
02:30
So once again we start with an equal sign...