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

Alex made an error when looking up the probability on the Standard Normal Probabilities table.

Step-by-step explanation:

Standard Normal Probabilities refer to the probabilities associated with a standard normal distribution, often denoted as Z. These probabilities correspond to the area under the standard normal curve and are frequently used in statistical analysis and hypothesis testing to assess the likelihood of certain events occurring.

Alex correctly calculated the z-score for his home run hitting distance, which is -1.21. However, he made an error when looking up the probability on the Standard Normal Probabilities table. The correct probability for his home runs to travel at least 375 feet can be found by subtracting the probability corresponding to the z-score from 1. In this case, the correct probability is approximately 0.8869, not 0.1131.

Answer 2

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.