Answer to Question #104176 in Statistics and Probability for Katenda

Question

Question 21

Consider the information provided in question 20. What is the probability that the sample mean is at least 67.5?

(1) 2.5
(2) 0.9938
(3) 0.0062
(4) -2.5
(5) None of the above

Answer 1

2)0.9938

P(X$\geq$ 67.5)

Mean=70, sd=6, sample size =36

$Z=\frac {(X-\mu) *\sqrt n} {SD}$

$Z=\frac{(67.5-70)*\sqrt{36}}{6}$

=-2.5

$\Phi(2.5)$

The value is 0.9938 from the z-tables. The answer is (2) 0.9938.