Question

The weight of people in a small town in missouri is known to be normally distributed with a mean of 154 pounds and a standard deviation of 29 pounds. on a raft that takes people across the river, a sign states, "maximum capacity 3,460 pounds or 20 persons." what is the probability that a random sample of 20 persons will exceed the weight limit of 3,460 pounds? use table 1. (round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Answer 1

If a random sample of 20 persons weighed 3,460, the sample mean x-bar would be 3460/20 = 173 pounds.
The z-score for 173 pounds is given by:
$z=\frac{173-154}{29}=0.655$
Referring to a standard normal distribution table, and using z = 0.66, we find:
$P(\bar x\ \textless \ 173)=0.7454$
Therefore
$P(\bar x\ \textgreater \ 173)=1-0.7454=0.2546$
The answer is: 0.2546