Answer to Question #97569 in Statistics and Probability for Juliet Beglaryan

Question

3. During calendar year 2016 the candidates for the Certified Public Accountant (CPA) exam had taken an average of 141.3 semester hours of credit with a standard deviation of 17.77 credit hours. If a random sample of =64 201 8 6 CPA exam candidates is selected, what is the probability that the sample mean number of credit hours is between 137 and 144?

Answer 1

Let $X=$ the number of credit hours: $X\sim N(\mu,\sigma^2).$

Then

$$Z={X-\mu \over \sigma}\sim N(0, 1)$$

Given that

$$\mu=141.3, n=64, \sigma/\sqrt{n}=17.77/\sqrt{64}$$

$$P(137\leq X\leq144)=P\big({144-141.3 \over 17.77/8}\big)-P\big({137-141.3 \over 17.77/8}\big)=$$

$$=P(1.2155)-P(-1.9358)\approx0.887918-0.026443\approx$$

$$\approx0.8615$$

$P(137\leq X\leq144)=0.8615$