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- The price (in SEK) for a certain share is described by a lognormally distributed random variable Y=exp(X) where X is normally distributed with expected value my=5 and standard deviation sigma=0.5. a) What will be the expected value and standard deviation of Y? b) What is the probability that the share price exceeds SEK 155 c) What is the 95th percentile for the stock price?The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last a.) less than 8 months b.) between 8 and 12 months.assume that X is normally distributed with a mean 180 and standard deviation of 56. find the probability that (A) x is less then 115and (B) x is grater then 154
- The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.assume that X is normally distributed with a mean 150 and standard deviation of 40. find the probability that (A) x is less then 158 and (B) x is grater then 178assume that X is normally distributed with a mean 160 and standard deviation of 45. find the probability that (A) x is less then 159 and (B) x is grater then 160
- Suppose X is a randomvariable of normal distribution with mean equal to -2 and standard deviation equal to 4. Find P(X>-2)X is a normally normally distributed variable with mean u =10 and standard deviation a =4. Find A) P(x 1) C) P(103) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X < 70) c) The 95 th percentileThe random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630Write a function mysquares[v, m, μ, o] that constructs m samples of v sums-of-squares of the deviation from the mean (as in the workbook) with the X; drawn from the normal distribution N(μ, o). Also write histxsq[v, m, µ, σ] to plot a PDF histogram of your samples (with Automatic bspec), with the appropriate x² PDF plotted over the top. With m = 10 000, plot a few examples to see how well the x² distribution fits your samples. [Say v= 2, µ = 1, σ=2; v = 6, μ = 3, 0 = 10; v = 16, μ = 0, 0 = 1.]The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.62. a) find the P(10<x<15) (10 and 15 are seconds) b) find the P(x>15| x>10) (10 and 15 are seconds) c) find the P(x<15) (15 is seconds)