A family has two children. If the genders of these children are listed in the order they are born, there are four possible outcomes: BB, BG, GB, and GG. Assume these outcomes are equally likely. Let X represent the number of children that are girls. Find the probability distribution of Y. Part: 0 / 2 Part 1 of 2 (a) Find the number of possible values for the random variable X. There are possible values for the random variable X. X 5Following is the probability distribution of a random variable that represents the number of extracurricular activities a college freshman participates in. X 0 1 2 3 4 P (x) 0.07 0.13 0.45 0.22 0.13 Send data to Excel Part: 0 / 3 Part 1 of 3 (a) Find the probability that a student participates in exactly three activities. The probability that a student participates in exactly three activities isA true-false quiz with 10 questions was given to a statistics class. Following is the probability distribution for the score of a randomly chosen student. Find the mean score and interpret the result. Round the answers to two decimal places as needed. X 5 6 7 8 9 10 P(x) 0.05 0.16 0.32 0.26 0.13 0.08 Send data to Excel The mean is X If we were to give this quiz to more and more students, the mean score for these students would approachDetermine whether the random variable described is discrete or continuous. The weight of a block of tofu. The random variable described is (Choose one)Determine whether the random variable described is discrete or continuous. The number of pets a randomly chosen family may have. The random variable described is (Choose one) XDetermine whether the table represents a discrete probability distribution. Explain why or why not. P (x) 30 0.2 40 0.2 50 0.2 60 0.2 70 0.2 Send data to Excel The table (Choose one) represent a discrete probability distribution because (Choose one)Compute the mean and standard deviation of the random variable with the given discrete probability distribution. X P(x) -7 0.26 -3 0.13 2 0.25 7 0.28 8 0.08 Send data to Excel Part 1 of 2 (a) Find the mean. Round the answer to three decimal places, if necessary. The mean is X 5 Part 2 of 2 (b) Find the standard deviation. Round the answer to three decimal places, if necessary. The standard deviation isFifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. X 0 2 3 4 P(x) 0.05 0.25 0.30 0.20 0.10 0.10 Send data to Excel Part: 0 / 4 Part 1 of 4 (a) Find P (2). P (2) = X 5Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. 0 2 3 4 5 P ( x ) 0 .10 0.30 0.25 0.25 0.05 0.05 Part: 0 / 3 Part 1 of 3 (a) Compute the mean up. Round the answer to three decimal places as needed. Hy = X 5Relax! A recent survey asked 1685 people how many hours per day they were able to relax. The results are presented in the following table. Number of Hours Frequency 114 185 339 252 318 234 149 31 63 Total 1685 Send data to Excel Consider these 1685 people to be a population. Let X" be the number of hours of relaxation for a person sampled at random from this population. Part 1 of 5 (a) Construct the probability distribution of X: Round the answer to three decimal places. X 0 1 2 3 5 6 X 5 P(x) Part 2 of 5 (b) Find the probability that a person relaxes more than 3 hours per day. The probability that a person relaxes more than 5 hours per day is .( Round the answer to three decimal places.) X 5 Part 3 of 5 (c) Find the probability that a person doesn't relax at all. The probability that a person doesn't relax at all is .( Round the answer to three decimal places.) X 5 Part 4 of 5 (d) Compute the mean u . Round the answer to two decimal places. Hy = X 5 Part 5 of 5 (e) Compute the standard deviation op. Round the answer to three decimal places.School days: The following table presents the numbers of students enrolled in grades 1 through 8 in public schools in a certain country Grade Frequency (in 1000s) 3748 3644 3620 3586 3605 3666 3713 3762 Total 29,344 Send data to Excel Consider these students to be a population. Let X be the grade of a student randomly chosen from this population. Part: 0 / 5 Part 1 of 5 (a) Construct the probability distribution of X. Round the answer to three decimal places. X 2 3 4 5 6 7 8 X 5 P(x)Lottery: In the New York State Numbers lottery, you pay $2 and can bet that the sum of the numbers that come up is 13 . The probability of winning is 0.065 , and if you win, you win $8, which is a prot of$6. If you lose, you lose 32. (a) What is the expected value of your prot? Round the answer to two decimal places. The expected value of prot is E]. l Insurance: An insurance company sells a 1year term life insurance policy to an 84yearold man. The man pays a premium of $1900 . If he dies within 1 year, the company will pay $30,000 to his beneciary. According to the U.5. Centers for Disease Control and Prevention, the probability that an 84 yearold man will be alive 1 year later is 0.9381 . LetX be the prot made by the insurance company. (a) Find the probability distribution. The probability distribution is .5...- PW E] E]