Question

Consider the approximately normal population of heights of male college students with mean μ = 66 inches and standard deviation of σ = 4 inches. A random sample of 25 heights is obtained.

(a) Describe the distribution of x, height of male college students.

-skewed right

-approximately normal     

-skewed left

-chi-square

(b) Find the proportion of male college students whose height is greater than 74 inches. (Give your answer correct to four decimal places.)

(c) Describe the distribution of x, the mean of samples of size 25.

-skewed right

-approximately normal     

-skewed left

-chi-square

(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 > 71). (Give your answer correct to four decimal places.)


(f) Find P(x < 64). (Give your answer correct to four decimal places.)

Answer 1

(a) Describe the distribution of x, height of male college students.

Ans : approximately normal

(b)

Given that X follows a Normal distribution with Mean 66 Note thatz-(x-A)/σ-(x-66)/4 (Eq.1) follows standard Normal. Whenx 74, from (Eq.1), z 2 P(X > 74)-P(Z > 2)-1-P(Z<2-1-0.9772-0.0228 (ans)

(c) Describe the distribution of x, the mean of samples of size 25.

Ans : approximately normal  

(d)