Aski gondola carries skiers to the top of a mountain. assume that weights of skiers are normally distributed with a mean of 199 lb and a standard deviation of 41 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 1. (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 . 8944. (round to four decimal places as needed.) d. is the new capacity of 20 passengers safe? since the probability of overloading is over 50 % comma the new capacity appears to be safe enough.

Maximum Mean weight of the passenger filled to the stated capacity of passengers is

A) Maximum mean weight of passengers =

Maximum mean weight of passengers =

Maximum mean weight of passengers

B)  First, find the z-score:

We need to find

Now, look at a standard normal table to find , therefore:

Hence, the probability that the mean weight of randomly selected skiers exceeds is about %

C) With only passengers, the new maximum mean weight of passengers =

Repeat the steps of point B)

Hence, the probability that the mean weight of randomly selected skiers exceeds is about %

D) The mean weight of skiers is , therefore:

number of passengers = l                            

The new capacity of skiers is safer than skiers, but we cannot consider it safe enough, since the maximum capacity should be of skiers.

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step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.