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. X P(x) 0 1 0.346 0.167 2 0.176 3 0.126 4 0.185 P (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
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Q: In the following probability distribution, the random variable x represents the number of activities…
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Answer: - Given probability distribution
X | 0 | 1 | 2 | 3 | 4 |
P(X) | 0.346 | 0.167 | 0.176 | 0.126 | 0.185 |
Verify that this is a discrete probability distribution.
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- Dirty air: The federal government has enacted maximum allowable standards for air pollutants such as ozone. Let X be the number of days per year that the level of air pollution exceeds the standard in a certain city. The probability distribution of X is given by x 0 1 2 3 4 Px 0.34 0.39 0.17 0.06 0.04 1. Find P(3) 2. Find P(2 or fewer). 3. Find the probability that the standard is exceeded on at least one day. 4. Find the probability that the standard is exceeded on more than one day. 5. Compute the mean ux. Round the answer to two decimal places. 6.Compute the standard deviation σx. Round the answer to three decimal places.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.Consider the following discrete probability distribution. x 33 34 35 36 37 38 39 40 P(x) 0.02 0.06 0.10 0.20 0.24 0.26 0.10 0.02 (a) Find the probability that the random variable x is at most 38. Don't round. (b) Find the probability that the random variable x is at least 35. Don't round.Let X be the number of applicants who apply for a senior level position at a large multinational corporation. The probability distribution of the random variable X is given in the following table. The outcomes (number of applicants) are mutually exclusive. Complete the table by calculating the cumulative probability distribution of X. Probability distribution Cumulative probability distribution The probability that there will be at least two applicants is The probability that there will be three or four applicants is 0 0.45 Outcome (Number of applicants) 1 3 0.30 2 0.15 0.08 and the probability that there will be at most three applicants is 4 0.02
- The number of courses (X) that Solano College sociology students are enrolled in this semester is approximated by the following probability distribution. For a randomly selected Solano College sociology class containing 36 students, find the narrowest interval that would accurately predict the mean number of courses that these students are enrolled in this semester 92% of the time. x p(x) 2 7% 3 19% 4 42% 5 21% 6 11%The following table lists certain values of x and their probabilities. Verify whether or not it represents a valid probability distribution. P(x) 0 0.31 1 0.30 2 0.19 3 0.16 The table a valid probability distribution.The table shows the various sums of money that can be won in playing a certain game and the associated probabilitics of winning each amount. To play the game players must purchase a ticket for $350. 20000 2000 | 1000 | 200 X(in$"s) P(X) 0.004 0.026 0.07 | 0.6 2b i. Find the value of b that will make the distribution a probability distribution. ii. Which amount is most frequently won by the players of the game? iii. Determine the standard deviation of the distribution
- In the following probability distribution, the random variable x represents the number of activities a parent of a 6th- to 8th-grade student is involved in. Complete parts (a) through () below. 3 0.099 P(x) 0.223 0.356 0.238 0.084 (a) Verify that this is a discrete probability distribution. This is a discrete probablity distribution because the sum of the probabilities is and each probability is (b) Graph the discrote probability distribution. Choose the correct graph below. O A O8. Oc. OD. 0.5 05- 0.5 0.5 04 04- 04 0.4 03 0.2- 0.3 0.3- 02 02 0.24 01- 01- 0.14 012 3 4 12 (c) Compute and interpret the mean of the random variable x. The mean is activities (Type an integer or a decimal. Do not round.) Ahinh nf the flnvatinn intnmentntinme of the mann ie nnenntPeople visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Entertainment Headquarters is given in the following table. There is a five-video limit per customer, so nobody ever rents more than five DVDs at a time. X (number of DVDs rented) 0 1 2 3 4 5 Probability P(x) 0.35 0.25 0.20 0.10 0.05 0.05 A) What is the expected number of DVDs rented per customer? B) What is the standard deviation of the number of DVD rentals per customer?The table defines a discrete probability distribution. Find the expected value of the distribution. x 0 1 2 3 Pr(x) 3/16 5/16 1/16 7/16