Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of

194

lb and a standard deviation of

37

lb. The gondola has a stated capacity of

25

passengers, and the gondola is rated for a load limit of

3750

lb. Complete parts (a) through (d) below.

**a.** Given that the gondola is rated for a load
limit of

3750

lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of

25

passengers?The maximum mean weight is

150

lb.

(Type an integer or a decimal. Do not round.)

**b.** If the gondola is filled with

25

randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)?The probability is

(Round to four decimal places as needed.)

**c.** If the weight assumptions were revised so
that the new capacity became

20

passengers and the gondola is filled with

20

randomly selected skiers, what is the probability that their mean weight exceeds

187.5

lb, which is the maximum mean weight that does not cause the total load to exceed

3750

lb?The probability is

(Round to four decimal places as needed.)

Answer #1

a)

maximum mean weight of the passengers if the gondola is filled to the stated capacity of25 passengers

=3750/25 =150

b)

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

here mean= μ= | 194 |

std deviation =σ= | 37.000 |

sample size =n= | 25 |

std error=σ_{x̅}=σ/√n= |
7.40 |

probability
=P(X>150)=P(Z>(150-194)/7.4)=P(Z>-5.95)=1-P(Z<-5.95)=1-0=1.0000 |

c)

sample size =n= | 20 |

std error=σ_{x̅}=σ/√n= |
8.2735 |

probability
=P(X>187.5)=P(Z>(187.5-194)/8.273)=P(Z>-0.79)=1-P(Z<-0.79)=1-0.2148=0.7852 |

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