Question

Alex's home run hitting distance is normally distributed with a mean of 410 feet and a standard deviation of 29 feet. He wanted to find the probability that his home runs traveled at least 375 feet. He calculated the z-score to be −1.21 and looked up the probability on the Standard Normal Probabilities table. He found that the table stated his probability as 0.1131. Determine whether Alex made an error in his calculation and explain.

Answer 1

The table value is not the probability Alex is looking for. It gives P(z < -1.21) and Alex wants P(z > -1.21). To finish his calculation, Alex needs to subtract the table value from 1.

If Alex made an error, it was that he took the table value as being the probability he wanted. It is not. All of his calculations so far are error-free. He isn't finished yet.

Answer 2

Answer with explanation:

Given : Alex's home run hitting distance is normally distributed with a mean of 410 feet and a standard deviation of 29 feet.

Let x be the random variable that represents the Alex's home run hitting distance.

He wanted to find the probability that his home runs traveled at least 375 feet.

i.e. $P(x\geq375)$

He calculated the z-score to be −1.21

That means he need to find $P(z\geq-1.21)$ corresponds to  $P(x\geq375)$

Now,  $P(z\geq-1.21)=1-P(z$ , here Ales made error , he calculated the Probability corresponding to $P(z$.