my dear student you posted multiple questions as per HomeworkLib rules I have solved the first one question Thank you.
7 Suppose X~N(4, 22). Using interactive standard normal table shown in class find the following probabilities...
Find the following probabilities for the standard normal distribution in R or using the standard normal table. Note I always recommend drawing the distribution. (Round your answers to four decimal places) ### Example R code mu-o: sigma = 1: x = x; # Note you will have to change the value of x. pnorm(x,mu.sigma) (a) PIX s 0.41) (b) P(X 2041) () PIXs-4.25) Find the following percentiles for the standard normal distribution in Ror using the standard normal table. (Round...
A) 0.7995 11. If Z is a standard normal variable find the probabilities of a) P(Z <-0.35)- @w B) 0.3982 C) 1.2008 D) p.4013 (2 points) b) P(0.25s Z<1.55) (3 points) c) P(Z > 1.55) (2 points) 12. Assume that X has a normal distribution with mean deviation .5. Find the following probabilities: 15 and the standard a) P(X < 13.50)- 3 points). b) P (13.25 <X < 16.50)- (5 points). B) 0 2706 C0 5412 D) 1.0824 A mountuin...
Using Excel - normal probabilities Consider the random variable x that follows a normal distribution, with a mean of μ = 54 and a standard deviation of σ = 4. You will select some of your answers to the questions that follow in this sample Excel spreadsheet: A B 1 P(x < 50.5) 2 P(49 < x < 51) In cell B1 of the sample spreadsheet, select the correct Excel formula for computing the probability that x is less than...
Given X is the normal with a mean of 22 minutes, and a standard deviation of 4 minutes. Find P(X<22.4) and P(X>22.4). Also, please sketch the normal distribution shape in both X-scale, Z-scale and show the area of interest?
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 8; σ = 2 P(7 ≤ x ≤ 11) = Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 6.0; σ = 1.4 P(7 ≤ x ≤ 9) = Assume that x has a normal...
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and standard deviation o = 1), then Y = X2 follows a chi-square distribution with 1 degree of freedom. In particular, show that My(t) = Mx2(t) = E[etX?), which equals the moment generating function of a chi-square distribution with 1 degree of freedom.
Suppose that X follows a normal distribution with a mean of 850 and a standard deviation of 100. Find P(823<X<917).
Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. P(x ≥ 6); μ = 17; σ = 5 0.486 0.243 0.986 0.493 0.014
3. (4 pts) Using a normal distribution having mean of 200 and standard deviation of 15.0, calculate the following probabilities: a. P(X <= 180) b. P(X<=220) c. P(X >= 220) d. P(180 <= X <= 220)
How can you find out the following probabilities assuming that you know the mean and standard deviation? P(X <= µ+2σ) = ? P(µ <= X <= µ+3σ) = ? P(|X - µ| <= 3σ) = ? P(|X - µ| > 3σ) = ? Consider two situations. One in which you do not know the probability distribution and another when the distribution is Normal.