In the following probability distribution, the random variable x represents the number of activities a parent of a K to 5th-grade student is involved in. Complete parts (a) through (f) below. 1 2 3 P(x) 0.295 0.255 0.194 0.173 0.083 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because the sum of the probabilities is and each probability is b) Compute and interpret the mean of the random variable x. between 0 and 1, inclusive. The mean is activities. Type an integer or a decimal.) greater than 0 and less than 1. greater than or equal to 0. (c) Compute the standard deviation of the random variable x. less than or equal to 1. The standard deviation is activities. Round to one decimal place as needed.)

Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. y 0 1 2 3 4 p(y) 0.63 0.21 0.11 0.03 ? (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) p(4) =  (b) How would you interpret  p(1) = 0.21? In the long run, the proportion that will have at most one broken egg will equal 0.21.In the long run, the proportion of cartons that have exactly one broken egg will equal 0.21.    The probability of one randomly chosen carton having broken eggs in it is 0.21.The proportion of eggs that will be broken in each carton from this population is 0.21. (c) Calculate  P(y ≤ 2),  the probability that the carton contains at most two broken eggs. P(y ≤ 2) =  Interpret this probability. The probability of two randomly chosen cartons having broken eggs in them is this probability.In the…

In the following probability​ distribution, the random variable x represents the number of activities a parent of a K to 5th​-grade student is involved in. Complete parts​ (a) through​ (f) below.

In the following probability distribution, the random variable x represents the number of activities a parent of a K to 5th-grade student is involved in. Complete parts (a) through () below. to 1 2 3 4 P(x) 0.299 0.084 0.131 0.213 0.273 (a) Verify that this is a discrete probability distribution. This is a discrete probability distribution because the sum of the probabilities is 1 and each probability is between 0 and 1, inclusive. (b) Graph the discrete probability distribution. Choose the correct graph below. YA. O B. OC. OD. 0.5- 04 Q 0.5- 0.5- 0.- 4- 0.4- 0.4- 0.4- 0.3- 0.3- 0.3- 0.3- 0.2+ 0.2- 0.2- 0.2- 0.1+ 0.1- 0.1- 0.1- 0- 0 1 0- 0 1 4 012 3 4 ó i 2 3 (c) Compute and interpret the mean of the random variable x. The mean is activities. (Type an integer or a decimal. Do not round.)

The joint probability distribution function of X and Y is given by: 1 2 3 1 0.05 0.06 0.10 X 2 0.13 0.21 0.30 a. Find the conditional distribution of Y given X = 1 b. Find the conditional distribution of X given Y = 2 5 0.02 0.03 0.10

Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15   Is this model a probability distribution? A. Yes. B. No. C. Maybe.

Assume that 12 jurors are randomly selected from a population in which 75% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. xx P(x)P(x) 0 0+ 1 0+ 2 0+ 3 0.0004 4 0.0024 5 0.0115 6 0.0401 7 0.1032 8 0.1936 9 0.2581 10 0.2323 11 0.1267 12 0.0317 Find the probability of exactly 8 Mexican-Americans among 12 jurors.P(x=8)=P(x=8)= Find the probability of 8 or fewer Mexican-Americans among 12 jurors.P(x≤8)=P(x≤8)= IncorrectDoes the occurrence of 8 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?

Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. xx P(x)P(x) 0 0+ 1 0+ 2 0+ 3 0.0001 4 0.0005 5 0.0033 6 0.0155 7 0.0532 8 0.1329 9 0.2362 10 0.2835 11 0.2062 12 0.0687 Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x=7)=P(x=7)= Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x≤7)=P(x≤7)= Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? no yes

Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. y 0 1 2 3 4 p(y) 0.63 0.19 0.11 0.05 ? (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) p(4) =   Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs. P(y ≤ 2) = Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. P(y < 2) =

In the probability distribution to the right, the random variable X represents the number of hits a baseball player obtained in a game over the course of a season. Complete parts (a) through (f) below. 10000 (Type an integer or a decimal. Do not round.) X 0 1 2 3 4 5 P(x) 0.1666 0.3358 0.2857 0.1481 0.0383 0.0255 games. OD. Over the course of many games, one would expect the mean number of hits per game to be the mean of the random variable. (d) Compute the standard deviation of the random variable X. x = hits (Round to three decimal places as needed.) (e) What is the probability that in a randomly selected game, the player got 2 hits? ☐ (Type an integer or a decimal. Do not round.) (f) What is the probability that in a randomly selected game, the player got more than 1 hit?