The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8 cm. a. Find the probability that an individual distance is greater than 214.80 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 203.70 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution.   The prices of photo printers on a website are normally distributed with a mean of ​$238 and a standard deviation of ​$67. Random samples of size 33 are drawn from this population and the mean of each sample is determined.

In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D. The lowest score that would qualify a student for an A is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a B is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a C is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a D is nothing. ​(Round up to the nearest integer as​ needed.)

For a population that has a standard deviation of 22​, figure the standard deviation of the distribution of means for samples of size​ (a)2​, (b)4​, (c)5​ and​ (d)10.