Find the probability, P(Z > -0.77) for a standard normal variable Z. 20 Find the probability, P(-1.11 < Z < 2.12) for a standard normal variable Z.

Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ between 93 and 117.

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 87th percentile.

What is the probability of a continuous Normal random variable given a value of the random variable?  What are the parameters?  Use a calculator and show the functions used to find P(X>10) given a mean of 25 and a standard deviation of 2.

a) Find  such that P( X < ? ) = 0.9332, where X is a normal random variable with mean = 10 and standard deviation  = 2.5.  b) Find  such that P( X > ?) = 0.1230, where X is a normal random variable with mean    = 10 and standard deviation  = 2.5.

Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood). The distribution of X for a healthy person is normally distributed with men u = 85 and standard deviation o = 25. A person suffers from severe excess in insulin would have a lower level of glucose. A blood test with result of X < 40 would be used as an indicator that medication is needed. (a) What is the probability that a healthy person will be suggested with medication after a single test? (b) A doctor uses the average result of 2 tests for diagnosis, that is X. The second test will be conducted one week after the first test, so that the two test results are independent. For many healthy persons, each has finished two tests, find the expectation and standard error of the distribution of X. (c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests is less than 40, that is X < 40, so to reduce the chance of…

X is a discrete random variable with the following PMF: P(X = -9.2) = 0.25 P(X = -2.5) = 0.25 P(X = 7.7) = 0.5 Find the standard deviation of X.

The random variable X is described by using the gamma distribution with α = 5 and  λ = 1. Find the standard deviation of X.

Consider a random variable X that follows a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 5. Calculate the probability that X is less than 40.

Assume the random variable X is normally​ distributed, with mean μ=47 and standard deviation σ=8. Find the 14th percentile.