Consider the approximately normal population of heights of m

Consider the approximately normal population of heights of male college students with mean = 65 inches and standard deviation of = 3 inches. A random sample of 17 heights is obtained
(b) Find the proportion of male college students whose height is greater than 67 inches. (Give your answer correct to four decimal places.

(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)
  

(ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)
  

(e) Find P(x > 72). (Give your answer correct to four decimal places.)
  

(f) Find P(x < 63). (Give your answer correct to four decimal places.)

Solution

Given mean = 65 inches and standard deviation of = 3 inches. n = 17

SD of the sample mean = /sqrt(17) = 0.728
(b) Find the proportion of male college students whose height is greater than 67 inches.

P(X>67) = P[z>(67-65)/3]=1-P[z<=(67-65)/3]=0.2525

Proportion of male college students whose height is greater than 67 inches = 25.25%

(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)

mean of the distribution = E(x-bar) = 65
  

(ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)

standard error =  /sqrt(17) = 0.728  

(e) Find P(x > 72). (Give your answer correct to four decimal places.)

P(X>72) =1-P(X<=72) = 1- P[z<= (72-65)/0.728]=0.0000
  

(f) Find P(x < 63). (Give your answer correct to four decimal places.)

P(X<63) =P[z<(63-65)/0.728]= 0.0030