Answer to Question #218768 in Statistics and Probability for Dio

Question

The mean annual cost of autobile insurance is R95. Assume that the population standard deviation is R14. What is the probability that a simple random sample of size 30 for automobile insurance policies will have a sample mean less than R90?

A.2.5560 B. 0.0250 C. -1.96

D.0.0205

E.0.9750

Answer 1

Let $X=$ a sample mean: $X\sim N(\mu, \sigma^2/n).$

Given $\mu=95, \sigma=14, n=30$

$$P(X<90)=P(Z<\dfrac{90-95}{14/\sqrt{30}})$$

$$\approx P(Z<-1.956152)\approx0.025224$$

B. 0.0250