Question

Consider the approximately normal population of heights of male college students with mean μ = 72 inches and standard deviation of σ = 8.2 inches. A random sample of 12 heights is obtained.

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

skewed right, approximately normal, skewed left

(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 12.

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.)


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


(f) Find P(x > 68). (Give your answer correct to four decimal places.)


(g) Find P(x < 68). (Give your answer correct to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 72

standard deviation = = 8.2

a)  approximately normal

b) P(x > 74 ) = 1 - p( x< 74 )

=1- p [(x - ) / < (74 - 72) /8.2 ]

=1- P(z < 0.24)

= 1 - 0.5948 = 0.4052

proportion = 0.4052

c) approximately normal

d)

n = 12

mean = =   = 72

e) standard error = = / n = 8.2 / 12 = 2.3671

f)

P( < 68 ) = P(( - ) / < (68 - 72) /2.3671 )

= P(z < -1.69)

= 0.0455

probability = 0.0455

g)

P( >68 ) = 1 - P( < 68 )

= 1 - P[( - ) / < (68 -72) /2.3671 ]

= 1 - P(z < -1.69)

= 1 -0.0455 = 0.9545

Probability = 0.9545