( 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 )