1.)A small grocery store is considering installing an express checkout

1.)A small grocery store is considering installing an express checkout

1.)A small grocery store is considering installing an express checkout line. Let X be the number of customers in the regular checkout line. Note that these numbers include the customers being served, if any. The probability distribution of X is given in the table below.x0123P(X=x)0.10.50.30.1What is the standard deviation of the random variable X?2.) Football teams toss a coin to see who will get their choice of kicking or receiving to begin a game. Unfortunately, the coin is not fair, and has a probability of .3 of showing up heads. If a team always guesses heads, what is the probability that they WON’T win the coin toss 2 games in a row?3.)Consider a binomial random variable X with n = 2 and p = 0.50.Find the mean and the standard deviation of X.4.) Consider a binomial random variable, where the probability of success on each trial is .7, and there are 10 different trials. What is the probability of having more than 5 successes?5.) Suppose that on a particular highway, it is observed that the speed of automobiles follows a normal distribution with a mean of 72 and a standard deviation of 5. If the speed limit is 70, what is the probability that a car will be traveling over the speed limit?6.) Suppose that on a particular highway, it is observed that the speed of automobiles follows a normal distribution with a mean of 72 miles per hour and a variance of 25. If the speed limit is 70, what is the probability that a car will be traveling within 5 miles per hour of the speed limit?