Question

NASA excludes anyone under 5'2" in height and anyone over 6'3" 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: ?-177.6 cm and ?-9.7 cm 20-29 year old females: H 163.2cm and 5-10.1cm We want to answer the question: What fraction of the young female adults is eligible to be an astronaut pilot by these height constraints? Restated, we want to find Pr(females)1157.5cm 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) height 190.5cm), (put the greater than and/or less (round to 2 decimals) (round to 2 decimals) sing the Statisticl Using the Statistical Table B: The standard normal (Z) distribution, Pr(Z<157.5) (report the exact number from the table, do not round) Pr(Z190.5)- Thus, the fraction of young female adults that are eligible to be an astronaut pilot based on height alone is as a percentage to one decimal) (report the exact number from the table, do not round) (report answer

Answer 1

To find the fraction of young female adults eligible to be astronaut pilots based on height alone, calculate two probabilities using the standard normal distribution table and subtract the result from 1. The fraction is approximately 97.72%.

Step-by-step explanation:

To find the fraction of young female adults who are eligible to be astronaut pilots based on height alone, we need to calculate two probabilities using the standard normal distribution table.

1. Calculate Pr(Z < lower bound): Using the table, find the corresponding value for the lower bound of 157.5cm. The value from the table is 0.0668.

2. Calculate Pr(Z > upper bound): Using the table, find the corresponding value for the upper bound of 190.5cm. The value from the table is 0.0228.

Finally, we can find the fraction of young female adults eligible to be astronaut pilots by subtracting Pr(Z > upper bound) from 1: 1 - 0.0228 = 0.9772.

Therefore, approximately 97.72% of young female adults are eligible to be astronaut pilots based on height alone.