Mathematics: Aski gondola carries skiers to the top of a mountain. it bears a plaque stating that the maximum capacity is 14 people or 2324 lb. that capacity will be exceeded if 14 people have weights with a mean greater than startfraction 2324 l b over 14 endfraction equals 166 lb. assume that weights of passengers are normally distributed with a mean of 177 lb and a standard deviation of 41.4 lb. complete parts a through c below. a. find the probability that if an individual passenger is randomly selected,

Aski gondola carries skiers to the top of a mountain.

ariqueen

13.03.2022

we need to find the probability that if an individual passenger is randomly selected, their weight will be greater than 166 lb.

Assume that weights of passengers are normally distributed with a mean of 177 lb and a standard deviation of 41.4 lb.

Mean = 177

standard deviation = 41.4

We find z-score using given mean and standard deviation

z = $\frac{(x-mean)}{standard deviation}$

= $\frac{(166- 177)}{41.4}$ = -0.265700

Probability (z>-0.26570) = 1 - 0.3974 (use normal distribution table)

= 0.6026

P(weight will be greater than 166 lb) = 0.6026

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