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 )
12 . Based on the performance of all individuals who tested between July 1 , 2012 and June 30 , 2015 , the GRE Verbal Reasoning scores are normally distributed with a mean of 150 and a standard deviation of 8.45 . ( https :// www . ets . org / s / gre / pdf / gre _ guide _ table1a . pdf ). Show all work . Just the answer , without supporting work , will receive no credit .