Question

You have a list of 600 random, normally distributed numbers with a mean of 10 and a standard deviation of 2. Which of these statements is true?

A. About 489 numbers would lie between the values 8 and 12.
B. About 408 numbers would lie between the values 6 and 10.
C. About 285 numbers would lie between the values 10 and 14.
D. Exactly 408 numbers would lie between the values 10 and 14. E. Exactly 285 numbers would lie between the values 8 and 12.

Answer 1

Answer: C. About 285 numbers would lie between the values 10 and 14.

Explanation:

Answer 2

The correct answer for this questions is (C).

For 600 random , normally distributed numbers with a mean of 10 and standard deviation of 2, we expect 47.5% of the numbers to lie between 10 and 14. It is a fact that a normal distribution will have 47.5% of the sample size lie between 2 standard deviations from the mean on either side of the mean. 34.13% of the sample lies within 1 standard deviation and another 13.59% percent lie between the first standard deviation and the next. One standard deviation on the right side of 10 lands us at 12. The other standard deviation lands us at 14

The calculation
`(285)/(600) =0.475=47.5\%`, tells that that C is correct. The correct answer is C),