Question

Consider the approximately normal population of heights of male college students with mean μ = 72 inches and standard deviation of σ = 3.2 inches. A random sample of 21 heights is obtained.

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

skewed rightapproximately normal    chi-squareskewed left

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


(c) Describe the distribution of x, the mean of samples of size 21.

skewed leftskewed right    chi-squareapproximately normal

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


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


(e) Find P(x > 71). (Round your answer to four decimal places.)


(f) Find P(x < 68). (Round your answer to four decimal places.)

Answer 1

µ = 72, σ = 3.2, n = 21

(a) Distribution of x: approximately normal

(b) Proportion of male college students whose height is greater than 74 inches, P(X > 74) =

= P( (X-µ)/σ > (74-72)/3.2)

= P(z > 0.625)

= 1 - P(z < 0.625)

Using excel function:

= 1 - NORM.S.DIST(0.625, 1)

= 0.266

(c) Distribution of x, the mean of samples of size 21: approximately normal

(d) Mean of the x distribution, µₓ = 72

(ii) Standard error of the x distribution, σₓ = σ/√n = 3.2/√21 = 0.6983 = 0.70

(e) P(X > 71) =

= P( (X-µ)/σ > (71-72)/3.2)

= P(z > -0.3125)

= 1 - P(z < -0.3125)

Using excel function:

= 1 - NORM.S.DIST(-0.3125, 1)

= 0.6227

(f) P(X < 68) =

= P( (X-µ)/σ < (68-72)/3.2 )

= P(z < -1.25)

Using excel function:

= NORM.S.DIST(-1.25, 1)

= 0.1056