( a) The steering committee of UMUC Green Solutions Team consists of 3 committee members. 10 people are interested in serving in the committee. How many different ways can the committee be selected?
( b) A bike courier needs to make deliveries at 6 different locations. How many different routes can he take?
9. Let random variable x represent the number of girls in a family of three children.
( a) Construct a table describing the probability distribution.
( b) Determine the mean and standard deviation of x.( Round the answer to two decimal places)
10. Mimi just started her tennis class three weeks ago. On average, she is able to return 20 % of her opponent’ s serves. Assume her opponent serves 10 times.
( a) Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials( n), probability of successes( p) and probability of failures( q), respectively?
( b) Find the probability that that she returns at least 1 of the 10 serves from her opponent
11. A research concludes that the number of hours of exercise per week for adults is normally distributed with a mean of 4 hours and a standard deviation of 3 hours. Show all work. Just the answer, without supporting work, will receive no credit.
( a) Find the 75th percentile for the distribution of exercise time per week.( round the answer to 2 decimal places)
( b) What is the probability that a randomly selected adult has more than 7 hours of exercise per week?( round the answer to 4 decimal places)