00:01
So here in this question the normal distribution data is given.
00:06
So in which mean mu is equal to 167 .2 and the standard deviation sigma is equal to 11 .2.
00:19
So here we need to calculate the probability that a random selected value is less than 199 .7.
00:27
Randomly selected value is the x which should be less than 199 .7 so what is the probability we need to calculate here so for calculating that we need to understand some terms in the normal distribution that is the normal distribution curve regulates the z score which is z is equal to x minus mu by sigma where x is the data value data value then mu is the mean sigma is the standard deviation and z is the standard score so these standard score values z values are available in the table data book for normal reshooter curve so we need to calculate the z value at x is equal to 199 .7 at x is equal to 199 .7 z is equal to 199 .7 minus mu value is 167 .2 by sigma is 11 .2 so if we we simplify that we'll get z is equal to 2 .90178 so now we need to calculate the probability of p of z less than is equal to 2 .90178 we can't directly find the probability of x less than 199 .7, but we can find the probability of z less than 2 .90718.
02:09
So we need to convert the value of x data value into a standard score value.
02:14
Then we can use either the table method, z tables to calculate the value of probability or else we can also use the excel sheet to calculate the probability.
02:27
So i'm going to use here the excel sheet.
02:29
So go to the excel sheet, select formulas, then insert function f of x, select this function norm s .d.
02:40
So it is a normal distribution function which gives us the value of z...