Question

Using the following information to answer questions 13 and 14.

For typical data sets the following rules of thumb hold:

65% of data are within the interval [Average - StDev, Average + StDev]
95% of data are within the interval [Average - 2*St Dev, Average + 2*StDev]

14. A recent ACT administered to a local high school yielded the following results:
Mean = 24.4 and Standard Deviation = 4.2. Which of the following is true? (5 points)

• a. 95% of the students scored between 16 and 32.8
• b. 65% of the students scored between 16 and 32.8
• c. 95% of the students scored between 16 and 33.8
• d. 95% of the students scored between 20.2 and 28.6

Answer 1

Answer

we have mean = 24.4 and standard deviation = 4.2

By rule of thumb, we know that 95% of the data falls within 2 standard deviation from the mean.

So, we will calculate 2 standard deviation from the mean

and

μ-20-24.4-( 4.2 * 2)-24.4-8.4-16

So, 95% of the data falls within 16 and 32.8 levels

option A is correct.