Question

We have a class of 10 students who all spent different amounts of time studying for a quiz. The number of minutes each student studied is listed in the table below. Calculate the standard deviation of the class study time. Remember this is a population, not a sample. Round your answer to the nearest whole minute.

Student	Minutes of Studying
Student 1	82
Student 2	110
Student 3	103
Student 4	106
Student 5	108
Student 6	80
Student 7	107
Student 8	77
Student 9	106
Student 10	121

1. The standard deviation of study time for the class is equal to ____ minutes

Part 2:

The height of men in this class is normally distributed with a mean of 71 inches and a standard deviation of 2 inches.

A) A man who has a height of 60 inches is which of the following: A. Shorter than average B. Taller than average C. Above average

B) Because the data are normally distributed we know that approximately ____% of the men in this class have heights between 69 and 73 inches.

C) A man with a height of 75 inches is ____ standard deviations above the mean.

D) The z-score for a man who is 78 inches is ______

Answer 1

Answer)

1)

Steps to calculate standard deviation

First we need to find the mean

Mean = (82 + 110....)/(10) = 100

Now we need to subtract mean from each and every observation and then we need to take the square and add them

(82-100)^2 + (110-100)^2 ...

= 1988

Now we need to divide this 1988 by number of observations that is by 10 and take.the square root

Standard deviation = √{1988/10} = 14.0996453856

Part 2)

Mean = 71

S.d = 2

A)

60 is shorter than average

B)

69 = 71 - 2

73 = 71 + 2

According to the emperical rule

If the data is normally distributed

Then 68% lies in between mean - s.d and mean + s.d

95% lies in between mean - 2*s.d and mean + 2*s.d

99.7% lies in between mean - 3*s.d and mean + 3*s.d

So,

Because the data are normally distributed we know that approximately 95% of the men in this class have heights between 69 and 73 inches.

C)

Z = (x - mean)/s.d

Z = (75-71)/2 = 2

So, a man with a height of 75 inches is 2 standard deviations above the mean

D)

Z = (78 - 71)/2 = 3.5