Reference no: EM131062647
Discrete Probability Distributions-
1. At a certain store the number of arrivals per minute during the day has the following distribution:
Number of arrivals, x 0 1 2 3 4 5 6
Probability, P(x) .10 .20 .25 .18 .14 .08 .05
Find the mean and standard deviation of the distribution.
2. A box contains 5 pennies, 13 dimes, 10 quarters and 2 half-dollars. A coin is selected from the box at random. Construct the probability distribution by filling in the table below and draw a graph for the data.
Type of coin selected, x Penny Dime Quarter Half-Dollar
Probability, P(x)
3. If 80% of all people over 60 are retired, find the following probabilities for a sample of 20 people. Use the binomial distribution
(a) Exactly 15 are retired.
(b) At least 15 are retired.
(c) At most 15 are retired.
4. If 40% of all commuters ride to work in carpools, find the probability that if 8 workers are selected:
a) exactly 5 will ride in carpools;
b) at most will ride in carpools;
c) at least 5 will ride in carpools.
5. If 80% of all job applicants are able to pass a computer literacy test, find the mean, variance and standard deviation of people who pass the examination in a sample of 150. Show all calculations.
6. Let X be a binomial random variable with n = 12 and p = 0.3. Find the following:
a) P(X = 7)
b) P(X < 4)
c) P(X > 8)
d) P(4 < X < 10)
7. Ray Allen, perhaps the best 3-point shooter over the last 10 years in the NBA, has a chance to shoot 4 free throws. He was fouled shooting a 3 point shot, and he gets to take a fourth shot due to a technical foul. Suppose that the probability that he makes a free throw is .9, and his free throws are independent of each other. Let X be the random variable that gives the number of free throws made in 4 attempts.
a) Give the possible values for X.
b) Obtain the probability distribution for x.
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