1. In a binomial situation, n = 4and p = 0.18.Determine the probabilities of the following events using the binomial formula. (Round the final answers to 4 decimal places.)

a. x = 2

Probability=

b. x = 3

Probability=

c. x 2

Probability =

d. x < 3

Probability =

2.A local courier service reports that 90% of bulk parcels within the same city are delivered within two days. Six parcels are randomly sent to different locations.

a. What is the probability that all six arrive within two days? (Round the final answer to 4 decimal places.)

Probability

b. What is the probability that exactly five arrive within two days? (Round the final answer to 4 decimal places.)

Probability

c. Find the mean number of parcels that will arrive within two days. (Round the final answer to 2 decimal place.)

Number of parcels=

d-1. Compute the variance of the number that will arrive within two days. (Round the final answer to 3 decimal places.)

Variance=

3.In a binomial distribution n = 10 and p = 0.45. Find the probabilities of the following events: (Round the final answers to 3 decimal places.)

a. x = 2.

Probability

b. x 2 (the probability that x is equal to or less than 2).

Probability

c. x 3 (the probability that x is equal to or greater than 3).

Probability

4.A manufacturer of window frames knows from long experience that 10% of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 13 window frames:

a. None will need adjustment? (Round the final answer to 3 decimal places.)

Probability

b. At least one will need adjustment? (Round the final answer to 3 decimal places.)

Probability

c. More than two will need adjustment? (Round the final answer to 3 decimal places.)

Probability

5.Steele Electronics Inc. sells expensive brands of stereo equipment in several shopping malls. The marketing research department of Steele reports that 40% of the customers entering the store that indicate they are browsing will, in the end, make a purchase. Let the last 29 customers who enter the store be a sample.

a. How many of these customers would you expect to make a purchase? (Round the final answer to the nearest whole number.)

Number of Customers

b. What is the probability that exactly six of these customers make a purchase? (Round the final answer to 4 decimal places.)

Probability

c. What is the probability 18 or more make a purchase? (Round the final answer to 4 decimal places.)

Probability

6.A population consists of 13 items, 8 of which are acceptable. In a sample of six items, what is the probability that exactly five are acceptable? (Round the final answer to 4 decimal places.)

Probability=

7.In a Poisson distribution, = 0.86. (Round the final answers to 4 decimal places.)

a. What is the probability that x = 0?

Probability

b. What is the probability that x > 0?

Probability

8.Automobiles frequently arrive at the Bronte exit of the Queen Elizabeth Way at the rate of six per minute. The distribution of arrivals approximates a Poisson distribution.

a. What is the probability that no automobiles arrive in a particular minute? (Round the final answer to 4 decimal places.)

Probability

b. What is the probability that at least five automobile arrives during a particular minute? (Round the final answer to 4 decimal places.)

Probability

9.Automobiles frequently arrive at the Bronte exit of the Queen Elizabeth Way at the rate of seven per minute. The distribution of arrivals approximates a Poisson distribution.

a. What is the probability that no automobiles arrive in a particular minute? (Round the final answer to 4 decimal places.)

Probability

b. What is the probability that at least five automobile arrives during a particular minute? (Round the final answer to 4 decimal places.)

Probability

10. It is estimated that 0.4% of the callers to the billing department of a local telephone company will receive a busy signal.

What is the probability that of today's 1180 callers at least 5 received a busy signal? Use the poisson approximation to the binomial.(Round the final answer to 4 decimal places.)

Probability

11. In a recent survey, 54% indicated chocolate was their favorite flavour of ice cream. Suppose that we select a sample of 19 people and ask them to name their favourite flavour of ice cream.

a. How many of those in the sample would you expect to name chocolate? (Round the final answer to 2 decimal place.)

Expected number of people

b. What is the probability exactly thirteen of those in the sample name chocolate? (Do not round the intermediate values. Round the final answer to 4 decimal places.)

Probability

c. What is the probability thirteen or more name chocolate? (Do not round the intermediate values. Round the final answer to 4 decimal places.)

Probability

12. A manufacturer of computer chips claims that the probability of a defective chip is 0.008. The manufacturer sells chips in batches of 1,000 to major computer companies.

a. How many defective chips would you expect in a batch? (Round the final answer to 2 decimal places.)

Number of chips

b. What is the probability that none of the chips are defective in a batch? (Round the final answer to 4 decimal places.)

Probability

c. What is the probability at least one chip is defective in a batch? (Round the final answer to 4 decimal places.)

Probability

13.Recent crime reports indicate that 17.5 motor vehicle thefts occur every hour in Canada. Assume that the distribution of thefts per hour can be approximated by a Poisson probability distribution.

a. Calculate the probability exactly four thefts occur in an hour.(Round the final answer to 5 decimal places.)

Probability

b. What is the probability there are no thefts in an hour? (Round the final answer to 5 decimal places.)

Probability

c. What is the probability there are at least 20 thefts in an hour? Use excel or online calculator to find the answer. (Round the final answer to 5 decimal places.)

Probability

14.According to the "January theory," if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 39 out of the last 49 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.50.

What is the probability that this could occur by chance? (Round the final answer to 4 decimal places.)

Probability

15. In the game of heads or tails, if two coins are tossed, you win $0.72 if you throw two heads, win $0.36 if you throw a head and a tail, and lose $1.08 if you throw two tails. What are the expected winnings of this game? (Round the final answer to 4 decimal places.)

Expected winnings=