in a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean…

in a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean of 69.3 inches and a standard deviation of 2.0 inches. a study participant is randomly selected. complete parts (a) through (d) below. (a) find the probability that a study participant has a height that is less than 65 inches. the probability that the study participant selected at random is less than 65 inches tall is 0.0158. (round to four decimal places as needed.) (b) find the probability that a study participant has a height that is between 65 and 70 inches. the probability that the study participant selected at random is between 65 and 70 inches tall is 0.6210. (round to four decimal places as needed.) (c) find the probability that a study participant has a height that is more than 70 inches. the probability that the study participant selected at random is more than 70 inches tall is . (round to four decimal places as needed.)

in a survey of a group of men, the heights in the 20 - 29 age group were normally distributed, with a mean of 69.3 inches and a standard deviation of 2.0 inches. a study participant is randomly selected. complete parts (a) through (d) below. (a) find the probability that a study participant has a height that is less than 65 inches. the probability that the study participant selected at random is less than 65 inches tall is 0.0158. (round to four decimal places as needed.) (b) find the probability that a study participant has a height that is between 65 and 70 inches. the probability that the study participant selected at random is between 65 and 70 inches tall is 0.6210. (round to four decimal places as needed.) (c) find the probability that a study participant has a height that is more than 70 inches. the probability that the study participant selected at random is more than 70 inches tall is . (round to four decimal places as needed.)

Answer

Explanation:

Step1: Recall probability relationships

The total probability under the normal - distribution curve is 1. We know the probability of being less than 65 inches ($P(X < 65)=0.0158$) and the probability of being between 65 and 70 inches ($P(65<X < 70)=0.6210$).

Step2: Use the formula $P(X>70)$

We know that $P(X < 65)+P(65<X < 70)+P(X > 70)=1$. So, $P(X > 70)=1-(P(X < 65)+P(65<X < 70))$.

Step3: Substitute the known values

Substitute $P(X < 65) = 0.0158$ and $P(65<X < 70)=0.6210$ into the formula: $P(X > 70)=1-(0.0158 + 0.6210)$. $P(X > 70)=1 - 0.6368=0.3632$.

Answer:

0.3632