Answer to Question #104175 in Statistics and Probability for Katenda

Question

Question 20

Consider a population with a mean of 70 and a standard deviation of 6. A random sample of size 36 is drawn. What is the probability that the sample mean is between 70.5 and 71.5 ?

(1) 0.9332
(2) 0.5000
(3) 0.6915
(4) 0.2415
(5) None of the above.

Answer 1

(4) 0.2415

P(70.5<X<71.5)

Mean=70, SD=6, n=36

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

$Z1=\frac {(70.5-70)*\sqrt{36}}{6} =0.5$

Z2=$\frac {(71.5-70)*\sqrt{36}}{6}$ =1.5

=$\Phi(1.5)-\Phi(0.5)$

Read from the z-tables

=0.933319-0.69146

=0.241

The closest answer is (4) 0.2415.