Basic Stat HW Ch 5

1. Consider the following probability distribution

a. Find the Expected Value of X, E (X)

b. Find the Variance of X

c. Find the Standard Deviation of X

d. Find P (X ≥ 3)

2. Consider the following probability distribution

a. Find the Expected Value of X, E (X)

b. Find the Variance of X

c. Find the Standard Deviation of X

d. Find P (X ≥ 4)

3. An FBI survey shows that 20% of all property crimes go unsolved. Suppose that in your town 5 such crimes are committed independently of each other. Assume a binomial distribution.

a. What is the probability that 2 of these 5 crimes will be solved?

b. What is the probability that at least 1 crime will be solved?

c. What is the expected number of crimes that are solved?

4. Suppose the number of individual plants of a given species we expect to find in a one-meter square quadrat follows the Poisson distribution with a mean of 3 plants.

a. What is the probability of finding that exactly 2 plants in a one-meter square?

b. What about the probability that at least 2 plants in a given one-meter square?

c. What is the probability that there are exactly 7 plants in two-meter squares?

5. Suppose that the probability of selling a defective item on a Friday is 0.3. There are 10 items in a store. Assuming a binomial distribution.

a. Find the probability that exactly 4 defective items will be sold on a Friday?

b. Find the probability that at most 1 defective item will be sold?

c. Find the expected number and standard deviation of defective items sold.

6. In an online shop, the average number of items returned by a customer is 4 per day. Use Poisson distribution to calculate the probability that

a. Exactly 3 items will be returned in a day.

b. At least 2 items will be returned in a day.

c. Exactly 4 items will be returned in 2 days.

7. The number of Emergency calls in Virginia has a Poisson distribution with a mean of 10 calls a day. Assume a Poisson distribution.

a. Find the probability of seven Emergency calls in a day.

b. Find the probability of No Emergency calls in a day.

c. Find the probability of more than one Emergency call in a day.

8. The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.45. You have 5 such alarms in your home and they operate independently. Assume a binomial distribution.

a. Find the probability that there is No smoke alarms.

b. Find the probability that there are more than four smoke alarms.

c. Find the probability that there is at least two smoke alarms.

9. You sell sandwiches. 70% of people choose chicken, the rest choose something else. Suppose 3 customers are selected. Assume a binomial distribution.

a. What is the probability of selling 2 chicken sandwiches?

b. What is the probability of selling at least one chicken sandwich?

c. What is the expected number of chicken sandwiches customers?

10. A​ government's Department of Transportation reported that in​ 2009, Kuwait airline led all airlines in​ on-time arrivals for flights, with a rate of 0.75 on time. Suppose that 5 flights are selected. Assume binomial distribution.

a. What is the probability that 3 flights will be on​ time?

b. What is the probability that at least 4​ flights will be on​ time?

c. What is the expected number of on-time flights?

11. A company publishes statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For one​ year, Car A had 1.65 problems per car. Let the random variable X be equal to the number of problems with a newly purchased model A car. Assume Poisson distribution.

a. What is the probability that the new car will have some problem?

b. What is the probability that for the model A there are 2 problems?

c. What is the probability that there are exactly 4 problems in 2 cars?

12. The probability that a medical doctor passes a UK med exam is 0.25. Assuming a Binomial probability distribution model, what is the probability that among the next 10 applicants

a. Exactly 8 will pass?

b. at least two will pass?

c. Exactly 7 will fail?

13. Motorists arrive at a Gulf gas station at a rate of 4 Motorists per minute. Assuming a Poisson probability distribution model,

a. What is the probability that exactly 2 motorists will arrive at the Gulf gas station during next one minute?

b. What is the probability that some motorists will arrive at the Gulf gas station during next one minute?

c. What is the probability that exactly 6 motorists will arrive at the Gulf gas station during the coming five minutes?

14. Births in a hospital occur randomly at an average rate of 1.8 births per hour. Assume that birth process is a Poisson random variable.

a. What is the probability of observing 4 births in a given hour at the hospital?

b. What about the probability of observing more than or equal to 2 births in a given hour at the hospital?

c. What is the expected number of births in two hours?