Question

In a survey in a group of men, the heights in the 20-29 age group were normally distributed with a mean of 69.6 inches and a standard deviation of 4.0 inches. What is the probability a randomly selected participant is less than 68 inches tall? Probability the selected person is between 68 and 71 inches? Probability the selected person is more than 71 inches tall?

A. ( P(X < 68) ), ( P(68 < X < 71) ), ( P(X > 71) )
B. ( P(X > 68) ), ( P(68 < X < 71) ), ( P(X < 71) )
C. ( P(X < 68) ), ( P(68 < X < 71) ), ( P(X < 71) )
D. ( P(X > 68) ), ( P(68 < X < 71) ), ( P(X > 71) )

Answer 1

a. X~ N(69.6, 4.0) b. To find the probability that a randomly selected participant is between 68 and 71 inches tall, use the z-score formula. c. To find the probability that a randomly selected participant is more than 71 inches tall, use the z-score formula.

Step-by-step explanation:

a. X~ N(69.6, 4.0)

b. To find the probability that a randomly selected participant is between 68 and 71 inches tall, we need to calculate the area under the normal distribution curve between these two values. We can use the z-score formula to standardize the values:
z1 = (68 - 69.6) / 4.0 = -0.4
z2 = (71 - 69.6) / 4.0 = 0.35
Using the z-table or a calculator, we can find the corresponding probabilities: P(68 < X < 71) = P(-0.4 < Z < 0.35) = 0.3632

c. To find the probability that a randomly selected participant is more than 71 inches tall, we need to calculate the area under the normal distribution curve to the right of 71. Again, we can use the z-score formula:
z = (71 - 69.6) / 4.0 = 0.35
Using the z-table or a calculator, we can find the corresponding probability: P(X > 71) = P(Z > 0.35) = 0.3632