Find the expected value for the random variable. 3) A business bureau gets complaints as shown in the following table. Find the expected number of complaints per day. Complaints per Day 1 3 4 5 Probability| 0.04 0.11 0.26 0.33 0.19 0.12

Discrete Probability Distributions Worksheet 1. You flip four coins. Let X, the random variable, be the number of heads on all four coins. a. List the sample space for the experiment. b. What are the possible values for x? c. Is the random variable, x, continuous or discrete? d. Construct a probability distribution for this experiment. (X) e. Construct a histogram for the probability distribution in the space below. 2. Determine if the following are probability distributions (if no, state why). а. X 6. P(X) 4/9 12 15 3. 6. 1 2 3 4 5 P(X) 3/10 1/10 1/10 2/10 3/10 20 30 40 50 1.1 0.2 0.9 0.3 (X)

Blood Types and Rh Factors In addition to being grouped into four types, human blood is grouped by its Rhesus (Rh) factor. Consider the figures below that show the distributions of these groups for Americans. A B АВ Rh + 37% 34% 10% 4% Rh - 6% 6% 2% 1% Source: www.infoplease.com Send data to Excel Choose 1 American at random. Find the following probabilities. Enter your answers as decimals rounded to 3 decimal places.

2. The probability model of the number of dinners that a typical American cook in a week is as follows. Number of dinners: 1 3 4 6. 7. Probability: 0.05 0.05 0.1 0.15 0.15 0.2 ? 0.2 Complete the probability table (find the missing probability)

Consider the list of numbers 2,3,4. The following table includes the 9 possible combinations of choosing two numbers, with replacement, from this list. The sample means for each combination have already been calculated. Sample Mean T 2 2.5 3 2.5 3 2 2.5 3 3.5 Sample 2,2 2,3 2,4 3,2 Use the table above to construct a probability distribution. Sample Mean 4 3,3 3,4 4,2 4,3 4,4 Frequency 1 2 q q co 2 1 3.5 3 8 3.5 4 P(x) X X X X X

There are two routes Jasmine can take to work. Route A has five stoplights. The probability distribution of how many lights at which she will need to stop is below. The average amount of time spent at each stop light on Route A is 30 seconds. Number of red lights 1 2 3 5 Probability 0.04 0.28 0.37 0.14 0.11 0.06 Route B has three stop lights. The probability distribution of Route B is below. The average wait time for these lights is 45 seconds. Number of red lights 1 3 Probability 0.09 0.31 0.40 0.20 Which route should she take?

K The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions. Complete parts (a) through (c) below. Click the icon to view the data for fatal crashes in 2016. (a) Among fatal crashes in unknown weather conditions, what is the probability that a randomly selected fatal crash occurs when it is dawn/dusk? The probability that a randomly selected fatal crash in unknown weather conditions occurs when it is dawn/dusk is approximately. (Round to three decimal places as needed.) Data table Weather Daylight Dark, but Lighted 5875 497 51 54 255 Normal Rain Snow/Sleet Other Unknown 14,307 875 219 125 810 (...) Dark 8151 681 156 220 548 Dawn/Dusk Other 1183 87 40 71 65 8 2 9 133 X

A used-car dealer gets complaints about his cars as shown in the table. Number of complaints per day 0 1 2 Probability 3 4 5 6 0.02 0.06 0.17 0.25 0.3 0.11 0.09 Find the expected number of complaints per day. The expected number of complaints per day is (Do not round your answer.)