Answer:
Option D) Yes, he made an error. Because he was seeking the probability that his home runs traveled at least 385 feet, he looked up −0.46 and failed to subtract the probability from 1. The correct probability is 0.6772.
Step-by-step explanation:
We are given that Evan's home run hitting distance is normally distributed with a mean of 398 feet and a standard deviation of 28 feet i.e. [tex]\mu[/tex] = 398 feet and [tex]\sigma[/tex] = 28 feet.
Also, He wanted to find the probability that his home runs traveled at least 385 feet. He calculated the z-score to be −0.46 and looked up the probability on the Standard Normal Probabilities table. He found that the table stated his probability as 0.3228 .
The probability he stated is wrong because as we know that probability that his home runs traveled at least 385 feet is given by P(X >= 385 feet) ;
where, X = home run is being hit
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
P(X >= 385) = P( [tex]\frac{X-\mu}{\sigma}[/tex] >= [tex]\frac{385-398}{28}[/tex] ) = P(Z >= -0.46) = P(Z <= 0.46) = 0.6772.
When looking at the z table we find that at 0.46 critical value of x, the probability area is 0.6772 .
