In: Statistics and Probability
Consider the approximately normal population of heights of male college students with mean μ = 64 inches and standard deviation of σ = 4.6 inches. A random sample of 10 heights is obtained.
(a) Describe the distribution of x, height of male college students.
skewed leftapproximately normal skewed rightchi-square
(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 10.
skewed rightapproximately normal chi-squareskewed left
(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 > 68). (Round your answer to four
decimal places.)
(f) Find P(x < 63). (Round your answer to four
decimal places.)
a) since, population is approx normal, so, distribution of x, height of male college students will be approx normal
b)
µ = 64
σ = 4.6
P ( X > 74 ) = P( (X-µ)/σ ≥ (74-64) /
4.6)
= P(Z > 2.17 ) = P( Z <
-2.174 ) = 0.0149
(answer)
c) approximately normal
d) mean of the x distribution=64
ii) standard error of the x distribution = std error = σ/√n= 1.45
e)
µ = 64
σ = 4.6
n= 10
X = 68
Z = (X - µ )/(σ/√n) = ( 68
- 64 ) / ( 4.6 /
√ 10 ) =
2.750
P(X ≥ 68 ) = P(Z ≥
2.75 ) = P ( Z <
-2.750 ) = 0.0030
(answer)
f)
µ = 64
σ = 4.6
n= 10
X = 63
Z = (X - µ )/(σ/√n) = ( 63
- 64.00 ) / ( 4.600
/ √ 10 ) =
-0.687
P(X < 63 ) = P(Z ≤ -0.687 )
= 0.2459
(answer)