Suppose that the height, in inches, of a 25-year-old man is a normal random variable with parameters mu=71

Daniaal Sanchez

Daniaal Sanchez

Answered question

2021-08-16

Suppose that the height, in inches, of a 25-year-old man is a normal random variable with parameters mu=71 and sigma^2=6.25 . What percentage of 25-year-old men are over 6 feet, 2 inches tall? What percentage of men in the 6-footer club are over 6 feet, 5 inches?

Answer & Explanation

Nathalie Redfern

Nathalie Redfern

Skilled2021-08-17Added 99 answers

Given: Height (in inches) of a 25 year man a normal random variable weather mean
μ=71 and variance σ2=6.25
To find: (a) What percentage of men are over 6 feet 2 inches
(b) What percentage of men in the 6 footer club are over 6 feet 5 inches
Solution: (a)To calculate the percentage of men, we first calculate the probability
P[Height of a 25 year old man is her 6 feet 2 inches]=P[X>74in]
P[X>74]=P[Xμσ>74712.5]
=P[Z1.2]
=1Φ(1.2)
=1-0.8849
=0.1151
Thus, the persentage of 25 ear old men that are above 6 feet 2 inches is 11,5%
(b)P[Height of 25 year old man is above 6 feet 5 inches given that he is above 6 feet]=P[X? 6th 5in -X?6th]
P[X>6th 5in|X>6th]=P[X>77X>72]P[X>72]
=P[X>77]P[X>72]
=P[Xμσ>77712.5]P[Xμσ>72712.5]
=P[Z>2.4]P[Z>0.4]
=1P[Z>2.4]P[Z>0.4]
=10.991810.6554
=0.00820.3446
=0.024 Thus, Percentage of 25 year old men in the 6 footer club that are above 6 feet 5 inches are 2.4%
Result:Thus, the persentage of 25 ear old men that are above 6 feet 2 inches is 11,5%
Thus, Percentage of 25 year old men in the 6 footer club that are above 6 feet 5 inches are 2.4%

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