Question

n a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 68.6 inches and a standard deviation of 4.0 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 66 inches. The probability that the study participant selected at random is less than 66 inches tall is ​(b) Find the probability that a study participant has a height that is between 66 and 71 inches. The probability that the study participant selected at random is between 66 and 71 inches tall is ​(c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than 71 inches tall

Answer 1

Solution :

Given that ,

mean = = 68.6

standard deviation = = 4

(a)

P(x < 66) = P((x - ) / < (66 - 68.6) / 4)

= P(z < -0.65)

P(x < 66) = 0.2578

Probability = 0.2578

The probability that the study participant selected at random is less than 66 inches tall is 0.2578

(b)

P( 66 < x < 71) = P((66 - 68.6)/ 4) < (x - ) / < (71 - 68.6) / 4) )

= P(-0.65 < z < 0.6)

= P(z < 0.6) - P(z < -0.65)

= 0.7257 - 0.2578

= 0.4679

Probability = 0.4679

The probability that the study participant selected at random is between 66 and 71 inches tall is 0.4679

(c)

P(x > 71) = 1 - P(x < 71)

= 1 - P((x - ) / < (71 - 68.6) / 4)

= 1 - P(z < 0.6)

= 1 - 0.7257

= 0.2743

P(x > 71) = 0.2743

Probability = 0.2743

The probability that the study participant selected at random is more than 71 inches tall 0.2743 .