Question

A ski 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, their weight will be greater than 166 lb.

nothing ​(Round to four decimal places as​ needed.)

Answer 1

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