Suppose x has a distribution with a mean of 20 and a standard deviation of 4. Random samples of size n = 64 are drawn. A USE SALT (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has Select--- v distribution with mean u = and standard deviation o, = (b) Find the z value corresponding to x = 19.5. (c) Find P(x < 19.5). (Round your answer to four decimal places.) P(x < 19.5) = (d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 19.5? Explain. O Yes, it would be unusual because less than 5% of all such samples have means less than 19.5. O No, it would not be unusual because more than 5% of all such samples hare means less than 19.5. O Yes, it would be unusual because more than 5% of all such samples have means less than 19.5. O No, it would not be unusual because less than 5% of all such samples have means less than 19.5.

Assume that females have pulse rates that are normally distributed with a mean of μ=74.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts​ (a) through​ (c) below. a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 80 beats per minute. b. If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 80 beats per minute. c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 265 feet and a standard deviation of 40 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 264 feet. Round to 4 decimal places.

The mean amount of time it takes a kidney stone to pass is 16 days and the standard deviation is 5 days. Suppose that one individual is randomly chosen. Let X = time to pass the kidney stone. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly selected person with a kidney stone will take longer than 12 days to pass it. c. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.