NASA excludes anyone under 5\'2\" in height and anyone over 63 from being an ast
ID: 3063560 • Letter: N
Question
NASA excludes anyone under 5'2" in height and anyone over 63 from being an astronaut pilot (NASA 2004). In metric units, these values for the lower and upper height restrictions are 157.5cm and 190.5cm, respectively. The distribution of American adult heights within a sex and age group is reasonably well approximated by normal distributions as follows 20-29 year old males. -177.6cm and -9.7cm 20-29 year old females: H 163.2cm and 5-10.1cm We want to answer the question: What fraction of the young male adults is eligible to be an astronaut pilot by these height constraints? Restated, we want to find Pr(males)1157 5cm the greater than and/or less than symbols in correct places) The standard normal deviate for the lower bound The standard normal deviate for the upper bound- One way to find the answer is 1-Pr(Z lower bound upper bound) Using the Statistical Table B: The standard normal (Z) distribution Pr(Z 157.5) Pr(Z>190.5) Thus, the percentage of young male adults that are eligible to be an astronaut pilot based on height alone is height 190.5cm], (put (round to 2 decimals) (round to 2 decimals) (report exactly the number from the table, do not round) (report exactly the number from the table, do not round) (report answer as a percent, rounded to one decimal place)Explanation / Answer
Answer to the question is as follows
1. Pr(males) = 157.5 cm < height < 190.5 cm
2.
Standard normal deviate for the lower bound = (157.5-177.6)/9.7 = -2.07
Standard normal deviate for the upper bound = (190.5-177.6)/9.7 = 1.33
Pr(X<157.5) = P(Z< -2.07) = 0.0192
Pr(X<190.5) = P(Z> 1.33) = 0.0918
Thus, the %gae of young... is 1- (.0192+.0918 ) = 0.8890 or 88.9% percentage
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