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

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

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

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

$$\approx0.8615$$

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