3. The frequency distribution below shows the distribution for IQ STAT 200 | Page 5

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.