16. Let Z be the standard normal variable. Find the values of z if z satisfies: a. P(Z>z) = .9678 b. P(-z

Consider the normal distribution with mean 52 and standard deviation 20. Find the area under the normal curve and above the interval ​[35​,∞​) on the horizontal axis.

Use Table A to find the value of a standard Normal variable that satisfies each of the given conditions. (Use the value of z from Table A that comes closest to satisfying the condition.) In each case, sketch a standard Normal curve with your value of z marked on the axis, bo Find the point with 75% of the observations falling below it. Give your answer to two decimal places. z =

What is the cumulative area under the standard normal curve between z- score -1 and z-score 1 ?

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)P(z ≥ 1.95) = Shade the corresponding area under the standard normal curve.

Find the z-score such that: (a) The area under the standard normal curve to its left is 0.8242z =  (b) The area under the standard normal curve to its left is 0.7284z =  (c) The area under the standard normal curve to its right is 0.346z =  (d) The area under the standard normal curve to its right is 0.4859z =

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability ataran that a given score is less than -0.82 and draw a sketch of the region.

A standard normal variable Z can be transformed to the normally distributed random variable X with only mean µ known. True or False

To join the Illuminati, you have to be richer than 84% of Americans. Assuming incomes are distributed normally, what z score would satisfy such a requirement? Show it on the density graph for the standard normal distribution. Label the z score, axes. Show one standard deviation for comparison

A shot is fired at a very large circular target. The horizontal and vertical coordinates of the point of impact are independent random variables each having a standard normal density. Here the center of the target is taken as the origin. What is the density function of the distance from the center of the target to the point of impact? What are the expected value and the mode of this distance?