Question

A survey found that women's heights are normally distributed with mean 63.5 in. and standard deviation 2.4 in. The survey also found that men's heights are normally distributed with mean 69.1 in. and standard deviation 3.6 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 55 in. and a maximum of 62 in. Complete parts (a) and (b) below. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park? The percentage of men who meet the height requirement is ____%. (Round to two decimal places as needed.) Since most men ____ (meet/do not meet) the height requirement, it likely that most of the characters are ▼ men/women. b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements? The new height requirements are a minimum of ___. and a maximum of ___

Answer #1

a)

for normal distribution z score =(X-μ)/σx | |

here mean= μ= | 69.1 |

std deviation =σ= | 3.6000 |

percentage of men meeting the height requirement

probability = | P(55<X<62) | = | P(-3.917<Z<-1.972)= | 0.0244-0= |
0.0244~ 2.44% |

Since most men do not meet the height requirement, it likely that most of the characters are women

b)

The new height requirements are a minimum of 63.2 and a maximum of 69.1

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