101. Suppose that P, the price of a certain commodity (in dollars), and S, its total sales (in 10,000 units), are ran- dom variables whose joint probability distribution can be approximated closely with the joint probability density 5pe s for 0.20 0 f(p,s) = elsewhere Find the probabilities that (a) the price will be less than 30 cents and sales will exceed 20,000 units; (b) the price will be between 25 cents and 30 cents and sales will be less than 10,000 units.

The time it takes to travel from my apartment to work is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability that my commute time tomorrow will take between 30 and 35 minutes?(please round your answer to 2 decimal places)

What is the probability that the total of two randomly chosen numbers exceeds 3, where the first number is chosen from a uniform distribution between 0 and 2, and the second number is selected from an exponential distribution with a mean of 1?

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.