The state test scores for 12 randomly selected high school...

The state test scores for 12 randomly selected high school seniors are shown on the right. Complete parts (a) through (c) below. 1429 Assume the population is normally distributed. (a) Find the sample mean. $\bar{x}$ = \boxed{} (Round to one decimal place as needed.) (b) Find the sample standard deviation. s = \boxed{} (Round to one decimal place as needed.) (c) Construct a 99% confidence interval for the population mean $\mu$. A 99% confidence interval for the population mean is ($\boxed{}$$\boxed{}$). (Round to one decimal place as needed.) 1227 989 692 726 832 723 744 541 621 1445 945

Transcript

00:01 In this question, we have to find out the value of sample mean, the standard deviation as well as the confidence interval.

00:07 So, let us see how we can do so.

00:08 In the first part, we can write that the value of sample mean will be here equals to summation of xi that is sum of all the values such that i is going from 1 to n and then in the denominator it will be n.

00:21 So, this very value is here going to be 1 0 and now here it is 9 3 3 divided by it will be here 12 and it is here going to come around 9 1 1 point it is 0 8.

00:34 So, now we can say that the standard deviation value will be here s square and that is equals to 1 divided by n minus 1 and it is here going to be summation.

00:45 Now, it will be here i is equals to 1 and then here it is n.

00:49 Now, it will be here xi raised to the power 2 minus it is 1 divided by n and then here it is going to be xi.

00:57 Now, in the denominator it will be i is equals to 1 and now here it is going to be n then it will be here raised to the power 2 and now here we can write that it is 1 divided by 12 minus 1 and then it will be here let us write.

01:11 So, this very value is here going to be 1 0 9 8 and now here it is basically 7 4 4 7 and now it is minus we can write it as 1 0 9 3 3 raised to the power 2 divided by it will be here 12 and this very value is here going to be 9 3 3 2 4 and then it is here point 8 0 sorry it is 8 1 0 6.

01:39 So, this is the value of s square where s square is the variance and now we need to calculate the value of sample standard deviation which is basically s.

01:47 So, it will be under root of the our value which is 9 3 3 2 4 and now it is here point 8 1 0 6.

01:55 So, this will be equals to 3 0 5 point and then if we round it off then it will be basically here 5.

02:02 So, this is the approximate value and we can put this very value inside a box in order to highlight it and we should also put the our value inside the box and it will be here like this...

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