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A discrete probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. The probabilities are determined theoretically or by observation .
Dr. Fidget developed a test to measure boredom tolerance. He administered it to a group of 20,000 adults between the ages of 25 and 65. The possible scores were 0, 1, 2, 3, 4, 5 and 6, with 6 indicating the highest tolerance for boredom. The results were as follows. Find the probability distribution for the scores and illustrate the distribution.
400 6 1,600 5 4,400 4 6,000 3 3,600 2 2,600 1 1,400 0 Number of Subjects Score Boredom Tolerance Test Scores for 20,000 Subjects
7.
Example: Boredom Tolerance Test 400 6 1,600 5 4,400 4 6,000 3 3,600 2 2,600 1 1,400 0 Number of Subjects Score Boredom Tolerance Test Scores for 20,000 Subjects
The probability distribution for the number of customers at the Sunrise Coffee Shop is shown here. Find the mean, variance and standard deviation of the distribution.
0.12 0.21 0.37 0.2 0.10 P(x) 54 53 52 51 50 Number of Customers, X
The expected value of a discrete random variable of a probability distribution is the theoretical average of the variable. The formula is = E(X) = ___________. The symbol E(X) is used for the expected value.
Example: If a 60-year-old buys a $1000 life insurance policy at a cost of $60 and has a probability of 0.972 of living to age 61, find the expectation of the policy.
At a carnival you pay $2.00 to play a coin-flipping game with three fair coins. On each coin on one side has the number 0 and the other side has the number 1. You flip the three coins at one time and you win $1 for every 1 that appears on top. Are your expected earnings equal to the cost to play?
A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have probability 0.70 of germinating. The biologist plants 10 seeds. What is the probability that exactly 8 seeds will germinate?
According to the Textbook of Medical Physiology, 5th edition, by Arthur Guyton, 9% of the population has blood type B. Suppose we choose 18 people at random from the population and test the blood type of each. What is the probability that three of these people have blood type B?
Providence Electronics receives 400 calls in a typical day. Seventy percent of callers have touch-tone phones. If x is the random variable representing the number of callers with touch-tone phones in a group of 400, find its mean and standard deviation.
: In a restaurant, a study found that 42% of all patrons smoked. If the seating capacity of the restaurant is 80 people, find the mean, variance, and standard deviation of the number of smokers. About how many seats should be available for smoking customers?
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