1. Calculate the Poisson distribution whose (Average Rate of Success)) is 3 & X (Poisson

Random Variable) is 6.

2. Customers arrive at a checkout counter according to a Poisson distribution at an average

of 7 per hour. During a given hour, what are the probabilities that

a) No more than 3 customers arrive?

b) At least 2 customers arrive?

c) Exactly 5 customers arrive?

3. Manufacturer of television set knows that on an average 5% of their product is defective.

They sells television sets in consignment of 100 and guarantees that not more than 2 set

will be defective. What is the probability that the TV set will fail to meet the guaranteed

quality?

4. It is known from the past experience that in a certain plant there are on the average of 4

industrial accidents per month. Find the probability that in a given year will be less that 3

accidents.

5. Suppose that the change of an individual coal miner being killed in a mining accident

during a year is 1.1499. Use the Poisson distribution to calculate the probability that in

the mine employing 350 miners- there will be at least one accident in a year.

6. The number of road construction projects that take place at any one time in a certain city

follows a Poisson distribution with a mean of 3. Find the probability that exactly five road

construction projects are currently taking place in this city. (0.100819)

7. The number of road construction projects that take place at any one time in a certain city

follows a Poisson distribution with a mean of 7. Find the probability that more than four

road construction projects are currently taking place in the city. (0.827008)

1. A fair coin is tossed 10 times. What is the probability that exactly 6 heads will occur.

2. If 3% of the electric bulbs manufactured by a company are defective find the probability

that in a sample of 100 bulbs exactly 5 bulbs are defective.

3. An oil exploration firm is formed with enough capital to finance 10 explorations. The

probability of a particular exploration being successful is 0.1. Find mean and variance of

the number of successful explorations.

4. Emily hits 60% of her free throws in basketball games. She had 25 free throws in last

week's game.

a) What is the expected number and the standard deviation of Emily's hit ?

b) Suppose Emily had 7 free throws in yesterday's game.What is the probability that she

made at least 5 hits?

5. A coin is loaded so that heads has 60% chance of showing up. This coin is tossed 3 times.

a) What are the mean and the standard deviation of the number of heads that turned out?

b) What is the probability that the head turns out at least twice?

c) What is the probability that an odd number of heads turn out in 3 flips?

6. According to the 2009 current Population Survey conducted by the U.S. Census Bureau,

40% of the U.S. population 25 years old and above have completed a bachelor's degree or

more. Given a random sample of 50 people 25 years old or above, what is expected

number of people and the standard deviation of the number of people who have

completed a bachelor's degree.

7. Joe throws a fair die six times and face number 3 appeared twice. It he incredibly lucky or

unusual?

8. If the probability of being a smoker among a group of cases with lung cancer is .6, what's

the probability that in a group of 8 cases you have; (a) less than 2 smokers? (b0 More

than 5? (c) What are the expected value and variance of the number of smokers?

9. The manufacturer of the disk drives in one of the well-known brands of microcomputers

expects 2% of the disk drives to malfunction during the microcomputer's warranty

Median 70.639 Mean 69.855 Sample Variance 110.370 Population Variance 108.163 Sample Standard Deviation 10.506 Population Standard Deviation 10.400 Subtitle: 3. Comparing Population and Sample: When we used the Random Number Generator, we specified a mean of 70 and a standard deviation of 10. 1. Write a sentence to compare the mean you calculated with the population mean of 70 we specified and explain why they are the same or not the same. 2. Write a sentence to discuss how the mean compares with the median. Discuss how you expected these two scores of central tendency to compare and why. 3. Write a sentence to compare the population variance and the sample variance. Discuss how you expected the two scores of spread to compare and why. 4. Write a sentence to discuss the relationship between the sample variance and the sample standard deviation, justified by calculation.If we have a sample of size 26 with average 15 and standerd deviation of 2.5 from Normal population which has unknown mean and variance. Find 99% confidence interval for the population mean ? Use suitable critical values (za/, =2.58, OR ( (0/3,29) =2.787) (15.00, 29.99) O (6.98, 16,01) (13.63, 16.36) (11.98, 15.01)Sucrose Data Table Glucose Data Table Bubble Mean Bubble Mean Repetitions height Mean Measurement Deviation Repetitions Mean Measurement Deviation! (mm) Deviation height (mm) Deviation 0.0630 0.0790 0.0620 2 0.0780 3 0.1040 0.1080 Sum of Squared Sum of Squared Deviations Deviations # di observations " di [observations Median Median Range Variance Flange Variance Standard Deviation Standard (SD) Deviation (SD) Standard Error of the Standard Error of mean (SEM] the maan [SEM)You need to show all of your work or you will not get full credit! Please round all calculations to the hundredths place, for example 25.6775 would be rounded to 25.68. 7. The following SAMPLE scores are test grades from the first statistics exam. 45 50 65 65 70 70 75 80 85 90 95 100 a. Compute the mean, median, and mode. Mean= Median= Mode= b.Compute the SS, sample variance and sample standard deviation. Sums of Squares(SS)= Sample variance= Sample Standard Deviation=