Need Help with Statistics Homework

. What is a random variable? Choose the correct answer below. A. A random variable is a numerical measure, having values that can be plotted on a line in an uninterrupted fashion, of the outcome of a probability experiment. O B. A random variable is a numerical measure, having either a finite or countable number of values, of the outcome of a probability experiment. O C. A random variable is a numerical measure of the outcome of a probability experiment. 2. What are the two requirements for a discrete probability distribution? Choose the correct answer below. Select all that apply. [A. OSP(X) $1 B. 0

0. O B. The random variable is discrete. The possible values are d = 1, 2, 3, ... O C. The random variable is continuous. The possible values are d > 0 D. The random variable is continuous. The possible values are d = 1, 2, 3, .... 4. Determine whether the distribution is a discrete probability distribution. X P(x) 0.22 0.29 0.12 0.10 Is the distribution a discrete probability distribution? O A. Yes, because the sum of the probabilities is equal to 1. O B. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive. O C. No, because the sum of the probabilities is not equal to 1. D. Yes, because each probability is between 0 and 1, inclusive 5. The following data represent the number of games played in each series of an annual tournament from 1933 to 2005. Complete parts (a) through (d) below. x (games played) |4 Frequency 19 16 22 15 (a) Construct a discrete probability distribution for the random variable x. x (games played) P(x) (Round to four decimal places as needed.) (b) Graph the discrete probability distribution. Choose the correct graph below. OA. OB. O C. OD. AP( X ) AP(X ) 0.5 APEX ) (c) Compute and interpret the mean of the random variable x. Hx = games (Round to four decimal places as needed.) Interpret the mean of the random variable x. A. The series, if played many times, would be expected to last about 5.5 games, on average. O B. The series, if played one time, woul ed to last about 5.5 games. O C. The series, if played many times, would be expected to last about 4.5 games, on average. (d) Compute the standard deviation of the random variable x. _ games (Round to one decimal place as needed.) 6. The graph of the discrete probability to represents the number of live births by a mother 44 to 49 years old who had a live birth in 2015. Complete parts (a) through (d) below. Probability (a) What is the probability that a randomly selected 44- to 49-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? _(Type an integer or a decimal.) (b) What is the probability that a randomly selected 44- to 49-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? (Type an integer or a decimal.) (c) What is the probability that a randomly s ected 44- to 49-year-ol or more live birth in that year? ther who had a live birth in 2015 has had her sixth _(Type an inte d) If a 44- to 49-year-old mother who had a live birth in 2015 is randomly selected, how many live births would you expect the mother to have had? (Round to one decimal place as needed.) Suppose a life insurance company sells a $170,000 one-year term life insurance policy to a 24-year-old female for $270. The probability that the female survives the year is 0.999648. Compute and interpret the expected value of this policy to the insurance company. The expected value is $ Round to two decimal places as needed.) Which of the followin O A. The insurance company expects to m ge profit of $24.54 on every 24-year-old female it insures for 1 month. O B. The insurance company expects to age profit of $269.90 on every 24-year-old female it insures for 1 year. O C. The insurance company expects to ma e an average profit of $19.11 on every 24-year-old female it insures for 1 month. D. The insurance company expects to make an average profit of $210.16 on every 24-year-old female it insures for 1 year. An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $50.000. It the economy grows at a moderate pace, the investment will result in a profit of $20.000. However, there is a 30% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. What is the expected profit from this investment? The expected profit is $_ (Type an integer or a decimal.) 9. In the game of roulette, a player can place a $8 bet on the number 3 and have a 38 probability of winning. If the metal ball lands on 3, the player gets to keep the $8 paid to play the game and the player is awarded an additional $280. Otherwise, the player is awarded nothing and the casino takes the player's $8. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? The expected value is $ (Round to the nearest cent as needed.) The player would expect to lose about $ Round to the nearest cent as needed.)