question 1

An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string of the sort owe (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). For each outcome, let / be the random variable counting the number of even rolls in each outcome. For example, if the outcome is ooo, then N (ooo) = 0. Suppose that the random variable X is defined in terms of N as follows: X"=3N-N -4. The values of X are given in the table below. Outcome vee oeo eeo Bee ove eve ooo eoo Value of X -2 -2 -4 - 2 -2 -4 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X X 5 ? P(X=x) 0Not all visitors to a certain company's website are customers or potential customers. In fact, the company's executives estimate that about 12% of all visitors to the website are looking for other websites. Assume that this estimate is correct and that a random sample of 40 visitors to the website is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of visitors in the sample who actually are looking for the company's website by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. [I] (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. Anita's, a fastfood chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of instore play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that 48% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of4 customers at Anita's, exactly 2 order their food to go? Round your response to at least three decimal places. (If necessary, consult a list of formulas.) [D x b 9