Answer to Question #338418 in Statistics and Probability for Sami

Question

An aptitude test for selecting officers in a bank was conducted on 1,000 candidates, the average score is 42 and the standard deviation of scores is 24. Assume that the scores are normally distributed, answer the following questions.

i. What is the probability that the candidates score,

A. Exceed 65?

B. Between 40 and 60?

ii. Find the number of candidates whose score,

A. Exceed 40?

B. Lie between 40 and 65?

Answer 1

Let $X=$ score: $X\sim N(\mu, \sigma^2).$

Given $\mu=42,\sigma=24.$

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.

$$P(X>40)=1-P(Z\le\dfrac{40-42}{24})$$

$$\approx0.5332$$

$$0.5332(1000)=533$$

533 candidates

d.

$$P(40<X<65)=P(Z<\dfrac{65-42}{24})$$

$$-P(Z\le\dfrac{40-42}{24})\approx0.3643$$ $$0.3643(1000)=364$$

364 candidates