yes STA 2023 - Spring 2018 Ret #7097 Test: EXAM3 This Question: 1 pt Martha Luz

Question

yes STA 2023 - Spring 2018 Ret #7097 Test: EXAM3 This Question: 1 pt Martha Luz Bozzi & 1 4/7/18 1:54 PM Submit Test This Test: 25 pts possible A ski gondola carries skiers to the top of a mountain. Assume that s weights of skiers are normally distributed with a mean of 196 Ib and a standard deviation of 35 Ib The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 b a. Given that the gondola is rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers f the gondola is filled to the stated capacity of 25 e parts (a) through (d) below passengers? The maximum mean weight isb. (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 illed with 20 randomly selected skiers, what is the probability that their mean weight exceeds 187.5 b, which is the maximum mean weight that does not cause the total load to exceed 3750 Ib? The probability is (Round to four decimal places as needed) d. Is the new capacity of 20 passengers safe? Enter your answer in each of the answer boxes O Type here to search

Explanation / Answer

Ans:

Given that

mean=196

standard deviation=35

a)Maximum mean weight=3750/25=150

b)

z=(150-196)/(35/sqrt(25))

z=-6.57

P(z>-6.57)=1.0000

c)

z=(187.5-196)/(35/sqrt(25))

z=-1.214

P(z>-1.214)=0.8877

d)Not safe,as 88.77% of the time weight will exceed the mean capacity(187.5)

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