00:01
Hello student, the population of the values has a normal distribution with mean given mu is equal to 124 .2 and sigma is equal to 75 .5.
00:15
You intended to draw the random sample of the size n equal to 35.
00:20
Find the probability that the single random selected value is between let x be 121 .6 less than or equal to x less than or equal to 145 .9.
00:34
First make a transformation which is equal to question mark z is equal to x minus mu upon sigma.
00:41
We know that it is follow standard normal distribution and for that the probability is given in the statistical table.
00:48
Then 120 121 .6 minus mu upon sigma less than or equal to x minus mu upon sigma less than or equal to 145 .9 minus mu upon sigma.
01:03
Just put the values here we get 121 .6 minus 124 .2 upon sigma 75 .5 less than or equal to 145 .9 minus 124 .2 divided by 75 .5 which is equal to after simplifying we get this value as 0 .8 minus 0 .0344 less than or equal to z less than or equal to 0 .2874.
01:35
By using the formulas of the probability z is less than or equal to 0 .2874 minus square root of z is less than or equal to minus 0 .0344.
01:47
Subtract the probability from 1 we get it as a because in a statistical table priority of z greater than positive value or priority of z is less than negative value only probabilities are given.
02:01
Then we are changing it into the standard form.
02:06
Now it is in the standard form look at the priorities in the statistical table we get this probabilities as here written over here then finally we get this priority as 0 .1223.
02:26
Then next with the same number of randomly selected samples mean between then we have to find now probability of the mean is lies between the same values...