Question

According to a study by de Anna students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X=height of the individual.
a. X~__(—,—)
b. Find the probability that the person is between 65 and 69 inches. Include a sketch of the graph and write the probability statement.
c. The middle 40% of heights fall between what two values? Sketch the graph and write the probability statement.

Answer 1

a. X ~ N(66, 6.25)

b.$z_{1} =\frac{65-66}{2.5}=-0.4$
$z_{2} =\frac{69-66}{2.5}=1.2$
Using a standard normal probability table to find probability values for the z-scores, we get:
P(65 < X < 69) = 0.1554 + 0.3849 = 0.5403

c. z= 0.524 and -0.524
$0.524=\frac{X-66}{2.5}$
1.31 = X - 66
X = 67.31
When z = -0.524, X = 64.69.
P(64.69 < X < 67.31) = 0.4