The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 7.8 cm. a. Find the probability that an individual distance is greater than 207.50 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 193.50 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is (Round to four decimal places as needed.)

Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.   The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.90 years and a standard deviation of 1.80 years. Random samples of size 20 are drawn from the population and the mean of each sample is determined. Round the answers to the nearest hundredth.       Answer choices:  A.) 5.90 years , 0.40 years b) 5.90 years , 0.09 years c.) 1.32 years , 1.80 years d) 1.32 years , 0.40 years

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 270 feet and a standard deviation of 42 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X N( b. Find the probability that a randomly hit fly ball travels less than 302 feet. Round to 4 decímal places. c. Find the 90th percentile for the distribution of distance of fly balls. Round to 2 decimal places. feet

3. Assume the heights of students at Champlain College are normally distributed with a mean of 64.0 inchesand a standard deviation of 1.2 inches. Which of the following values best approximates the probabilityof randomly selecting a Champlain College studenttallerthan 62.2 inches?A. 0.0668B. 0.0359C. 0.9332D. 0.9641E. 1.0155