00:01
In this question, we are given a population of values follow a normal distribution with mean mu which is 42 .1 and sigma as a standard deviation 43 .9.
00:18
Random sample size n123 is drawn.
00:23
Given x is the value of a randomly selected element from the population.
00:29
So x will follow the normal distribution mean is 42 .1.
00:33
Variance will be sigma square that is 43 .9 square.
00:40
On the find probability a single randomly selected value is less than 35 .4.
00:46
So we're looking at probability of x less than 35 .4.
00:49
Now let's draw the distribution for x.
00:54
The mean here is 42 .1 and 35 .4 is over here and x less than this value is this shaded part here.
01:03
I'll be using the ti -84 calculator, the normal cdf function.
01:12
The lower limit to key in will be a large negative number.
01:16
So minus 10 to the power 99.
01:17
The upper limit to key in is 35 .4.
01:25
Mu here is the mean which is 42 .1.
01:29
Sigma here is the population standard deviation that is 43 .9.
01:36
When you click enter, you'll get this value which is 0 .4393, 4 decimal place.
01:47
Next, i'm going to let xi be the value of the i -th element in the sample.
01:53
I is from 1, 2 to 1, 2, 3 and m is the sample mean...