Question

As reported by a recent​ survey, the mean height of females 20 to 29 years old is μ=63.9

inches. If the height is approximately normally distributed with σ=2.8 inches, answer the following questions.

Click the icon to view a table of areas under the normal curve.

​(a) What is the percentile rank of a​ 20- to​ 29-year-old female who is 60.9 inches​ tall?

______th percentile ​(Round to the nearest integer as​ needed.)

​(b) What is the percentile rank of a​ 20- to​ 29-year-old female who is 70.1 inches​ tall?

______thpercentile ​(Round to the nearest integer as​ needed.)

​(c) What proportion of​ 20- to​ 29-year-old females are between 60.9 and 70.1 inches​ tall?

______th percentile ​(Round to four decimal places as​ needed.)

​(d) Would it be unusual for a​ 20- to​ 29-year-old female to be taller than 70.1inches?

A. No, because the probability of randomly choosing a​ 20- to​ 29-year-old female who is taller than

70.1 inches is less than​ 5%.

B. No, because the probability of randomly choosing a​ 20- to​ 29-year-old female who is taller than

70.1inches is greater than​ 5%.

C. Yes, because the probability of randomly choosing a​ 20- to​ 29-year-old female who is taller than

70.1 inches is less than​ 5%.

D. Yes, because the probability of randomly choosing a​ 20- to​ 29-year-old female who is taller than

70.1 inches is greater than​ 5%.

Answer 1

This is a normal distribution question with


a) P(x < 60.9)=?
The z-score at x = 60.9 is,

z = -1.0714
This implies that

14TH PERCENTILE

b) P(x < 70.1)=?
The z-score at x = 70.1 is,

z = 2.2143
This implies that
P(x < 70.1) = P(z < 2.2143) = \textbf{0.987}
99TH PERCENTILE

c) P(60.9 < x < 70.1)=?

This implies that
P(60.9 < x < 70.1) = P(-1.0714 < z < 2.2143) = P(Z < 2.2143) - P(Z < -1.0714)
P(60.9 < x < 70.1) = 0.986595925684541 - 0.14199480642940232

84TH PERCENTILE

d) P(x > 70.1)=?
The z-score at x = 70.1 is,

z = 2.2143
This implies that
P(x > 70.1) = P(z > 2.2143) = 1 - 0.986595925684541

C. Yes, because the probability of randomly choosing a​ 20- to​ 29-year-old female who is taller than 70.1 inches is less than​ 5%.

PS: you have to refer z score table to find the final probabilities.
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