Question

A professional baseball pitcher takes 14.61 seconds to throw each pitch, on average. Assume the pitcher's times per pitch follow the normal probability distribution with a standard deviation of 2.8 seconds. Complete parts a through d. a. What is the probability that a random sample of 10 pitches from this pitcher will have a mean less than 14 seconds? P(x< 14) = (Round to four decimal places as needed.) b. What is the probability that a random sample of 30 pitches from this pitcher will have a mean less than 14 seconds? PX< 14) = (Round to four decimal places as needed.) c. What is the probability that a random sample of 50 pitches from this pitcher will have a mean less than 14 seconds? PX< 14) = (Round to four decimal places as needed.) d. Explain the difference in these probabilities. Choose the correct answer below. O A. With a larger sample size, the standard error of the mean decreases and the sample means tend to move closer to the population mean of 14.61 seconds. Therefore, the probability of observing a sample mean less than 14 seconds decreases as the sample size increases. OB. With a larger sample size, the standard error of the mean stays the same and the sample means stay the same. Therefore, the probability of observing a sample mean less than 14 seconds decreases as the sample size increases. O c. With a larger sample size, the standard error of the mean increases and the sample means tend to move closer to the population mean of 14.61 seconds. Therefore, the probability of observing a sample mean less than 14 seconds decreases as the sample size increases. OD. With a larger sample size, the standard error of the mean increases and the sample means tend to move further away from the population mean of 14.61