Let X1, X2, ... X100 be 100 independent and identically distributed continuous random variables with mean = 37 and variance = 25. Let S = X1 + X2 + ... + X100. Use the Central Limit Theorem to approximate the probability that S is less than 3800 i.e. P(S<3800). Enter your answer to 4 decimal places. Hint: Calculate the mean and variance of S. By the Central Limit Theorem, S is approximately normally distributed with mean and variance vhen the sample size is larger than 30. In other words, standardization of S leads to S- Hs

he chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 10-year period. Assume each year is independent. Give the distribution of X.X ~

A snack company makes packages of grapes and honeydew slices. The weight of an individual package of grapes, G, is approximately Normally distributed with a mean of 3.25 ounces and a standard deviation of 0.91 ounces. The weight of an individual package of honeydew slices, H, is approximately Normally distributed with a mean of 4.51 ounces and a standard deviation of 2.02 ounces. Assume G and H are independent random variables. Let D = G – H. What is the probability that a randomly selected package of grapes weighs more than a randomly selected package of honeydew slices? 0.127 0.230 0.284 0.334