00:01
So i have a population of x values that is normally distributed with a mean equal to 151 .8 and a standard deviation of 37 .8.
00:14
And i want to find the probability that a single randomly selected value is between 107 .8 and 111 .4.
00:31
Well, that is the probability that 107 .8 minus the value of the mean mean divided by the value of the standard deviation is less than x minus the mean over the standard deviation less than 111 .4 minus the value of the mean divided by the value of the standard deviation.
00:59
And when x is normal, then x minus the mean divided by the standard deviation is your standard normal.
01:06
So this is the probability that a standard normal is between, let's see here, 107 .8 minus 151 .8 divided by 37 .8, negative 1 .16.
01:25
6 and on the right side i have let's see here 1 1 1 .4 so here i have negative 1 .07 and this is equal to 1 minus the probability that z is in the lower tail so less than negative 1 .16 six minus the probability that z is in the upper tail or actually these are both less than zero so let's do this differently this is the probability that z is less than negative one point zero seven minus the probability that c is less than negative 1 .16 because if we were to draw this, here is 0, here is negative 1 .07, here is negative 1 .16, and i want the area in between.
02:39
So if i take the larger area, which is this one, and subtract out the smaller tail which is this one then i end up with the area that i want so this then is let's see here these probabilities are in a standard normal table for 1 .07 your till probability is 0 .1423 and for 1 .16 the probability is 0 .123 so that means that the difference is 0 .0193.
04:07
And then for part b, we want for a randomly selected sample of size 212...