Answer to Question #337544 in Statistics and Probability for Jen

Question

A population of values has a normal distribution with u = 56.1 and o = 57.7. If a random sample of size n = 20 is selected,

- Find the probability that a single randomly selected value is greater than 63.8. Round your answer to four decimals

P(X > 63.8) =

-Find the probability that a sample of size n = 20 is randomly selected with a mean greater than

P(M > 63.8) =

Answer 1

1)

$$P(X>63.8)=1-P(Z\le\dfrac{63.8-56.1}{57.7})$$

$$\approx1-P(Z\le0.133449)\approx0.4469$$

2)

$$P(\bar{x}>63.8)=1-P(Z\le\dfrac{63.8-56.1}{57.7/\sqrt{20}})$$

$$\approx1-P(Z\le0.5968015)\approx0.2753$$