Compute the mean and variance of the discrete probability

1. Compute the mean and variance of the following discrete probability distribution.

X P(x)
2 .5
8 .3
10 .2

2. The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester based on past experience. What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation.

1000 .60
1200 .30
1500 .10

3. You are asked to match three songs with the performers who made those songs famous. If you guess, the probability distribution for the number of correct matches is:

Probability .333 .500 0 .167
Number correct 0 1 3 3

What is the probability you will get:
a) Exactly one correct?
b) At least one correct?
c) Exactly two correct?
d) Compute the mean, the variance, and the standard deviation of this distribution.

4. In a binomial situation n = 5 and p = .40. Determine the probabilities of the following events using the binomial formula.
a) x = 1
b) x = 2
c) x > 2
d) x 4

5. A local courier service reports that 95 percent of bulk parcels within the same city are delivered within 2 days. Six parcels are randomly sent to different locations.
a) What is the probability that all six will arrive within 2 days?
b) What is the probability that exactly five will arrive within 2 days?
c) Find the mean number of parcels that will arrive within 2 days.
d) Compute the variance and standard deviation of the number that will arrive within 2 days.

6. A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find:
a) The probability of making exactly 4 sales.
b) The probability of making no sales.
c) The probability of making exactly 2 sales.
d) The mean number of sales in the two-hour period.

7. In a Poisson distribution .
a) What is the probability that x = 2?
b) What is the probability that x 2?
c) What is the probability that x > 2?

8. Automobiles frequently arrive at the Bronte exit of the QEW at the rate of two per minute. The distribution of arrivals approximates a Poisson distribution.
a) What is the probability that no automobiles arrive in a particular minute?
b) What is the probability that at least one automobile arrive in a particular minute?

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