The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.57 inches and a standard deviation of 0.05 inch. A random sample of 10 tennis balls is selected. Complete parts (a) through (d) below. E> a. What is the sampling distribution of the mean? J" A. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will also be approximately normal. B. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will not be approximately normal. C. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 cannot be found. D. Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will be the uniform distribution. b. What is the probability that the sample mean is less than 2.56 inches? P()_( a. What is the probability that )_( is less than 49? P(:T a. If you select a random sample of 16 sessions, what is the probability that the sample mean is between 20.5 and 21.5 minutes? |:| (Round to three decimal places as needed.) The time to get an oil change at a certain car dealership averages 42.3 minutes with a standard deviation of 8.6 minutes. a) There are 45 cars booked for oil changes today. What is the probability that the jobs can be done in an average of 38 minutes or less? D Use 4 decimal places please. b} Suppose 90 oil changes were done in one particular week. There is a 95% chance that the mean time was more than minutes. D Use 1decimal place please. A random sample of n = 49 observations is drawn from a population with a mean equal to 24 and a standard deviation equal to 14. Complete parts a through 9 below. E> a. Give the mean and standard deviation of the (repeated) sampling distribution i. pea Gem (Type integers or decimals.) The average salary for a certain profession is $91,500. Assume that the standard deviation of such salaries is $30,500. Consider a random sample of 51 people in this profession and let x represent the mean salary for the sample. a Click the icon to view the table of normal curve areas. a. What is \"i? WED Suppose that a population is known to be normally distributed with p. = 2,500 and o = 250. If a random sample of size n = 8 is selected, calculate the probability that the sample mean will exceed 2,600. E) P()_( > 2,600) = D (Round to four decimal places as needed.) If a population is known to be normally distributed with p = 79 and 0' =18, what will be the characteristics of the sampling distribution for x based on a random sample of size 9 selected from the population? E> pi = D (Type an integer or a decimal.) If a population is known to be normally distributed with p = 72 and 0' = 32, what will be the characteristics of the sampling distribution for x based on a random sample of size 16 selected from the population? E> pi = E (Type an integer or a decimal.)