Answer to Question #335943 in Statistics and Probability for Sami

Question

average score is 42 and the standard deviation of scores is 24. Assume that the scores are

normally distributed answer the following questions

What is the probability that the candidates score

A. Exceed 65

B Between 40 and 60

Find the number of candidates whose score

A Exceed 407

Answer 1

A.

$$P(X>65)=1-P(Z\le\dfrac{65-42}{24})\approx0.1689$$

B.

$$P(40<X<60)=P(Z<\dfrac{60-42}{24})$$

$$-P(Z\le\dfrac{40-42}{24})\approx0.3066$$

C.

$$P(X>407)=1-P(Z\le\dfrac{407-42}{24})\approx0$$

There are no candidates whose score exceed 407.