2. Thesample data below shows the rental costs of one bedroom apartment in a town.

rental cost frequency

$1000 - 1200 5

1200 - 1400 8

1400 - 1600 10

1600 - 1800 7

Fine the mean and standard deviation.

3. In a local college, the survey data of smoking students is given below:

Smoking No smoking

Male 23 67

Female 35 65

Find the probability:

a) P (smoking given female) b) P (male and smoking) c)P (female or smoking).

4. In a surprise quiz, a student has never studied the subject and tries to answer allquestions in a random manner. The quiz has 8 questions where each question has 4multiple choices. Find the followings:

a) What is the probability that the student can have exactly 3 questions right?

b) How many questions do you expecthe or she would get right on average out of 8 questions?

5. The historical data of a company's annual sales is normally distributed with its mean,$350 million and its standard deviation, $32 million.

Find the probability that the company's sales will be higher than $ 420 next year?

6. Hershey's survey shows that Americans consumed an average of 11.4 pounds of chocolate per year with a standard deviation of 3.6 pounds. Assume that it is normally distributed. If you select randomly a person, what is the probability that he or she will consume

a) more than 9 pounds next year

b) between 7 and 12 pounds next year.

7. The top brand of a Toyota SUV's life is normally distributed with its mean, 18years and standard deviation, 4.5 years. Suppose that the top executives of the automakerdecided that only 2 % of new SUV sold could be replaced with a new car or fullyrefunded within the warranty period. What should be a reasonable warranty period?

8. The grade distribution of an Algebra course in a high school (total 1500 students)is normally distributed with its mean, 3.2 and standard deviation, 0.61.

1) If a student is randomly selected, find the probability that the student's score is higherthan 3.0?

2) If you collect a random sample of 30 students, what is the probability that the sample mean isless than 3.0?

9. In a ski resort area, the rental fee of two bedroom is known normally distributed but the true mean is unknown. A random sample of 12 rental fees in the area shows itsmean $550 and standard deviation $150 in winter. Find a 90% confidence interval estimate for the true mean.

10. A sample of 10 networking sites for a specific month has a mean number of visits of 26.1 and a standard deviation of 4.2. Find the 99% confidence interval of the true mean.

11. A U.S. Travel journal found that 39% said that they would take more vacations next year than this year. Find the 95% confidence interval for the true proportion of adults who said that they will travel more next year.

12. Determine the sample size needed to construct a 90% confidence interval to estimate the population mean when the population standard deviation is 805 and the margin of error is 14.

13. Determine the sample size needed to construct a 95% confidence interval to estimate the unknown population proportion when the sample proportion is 0.40 and the margin of error is 3%.

14. A recent report claims that the monthly sales of a McDonald store is less than $2 milliondue to Corona. A random sample of 35 stores shows that the sample mean is $1.80million and the standard deviation is $0.68 million. Prove the claim using the critical value methodat alpha = 0.10.

15. A Gallop poll in 2020 showed that Biden's popularity as the presidential candidate was 50%based on 1,024 people. Conduct a hypothesis test for the unknown population proportionclaiming that Biden's popularity washigher than 48% which is historically known as a sure-winning number. Use p-valuemethod at alpha = 0.05.

16. A company's top brand shows the following data of its unit selling price and itscorresponding sales amount:

Unit price ($) Sales amount ($million)

11 1.5

13 1.2

14 0.8

12 1.3

15 0.7

1) Find a simple linear regression model with X = unit selling price and Y = salesamount.

2) If the company lowers its selling price to $10, what would be the expected salesamount?

3) Based on the regression model you find, estimate the change of sales amount(increase or decrease) according to one dollar increase of product price.

4) As you know, the sales amount is affected by many different variables such asprice, advertising, quality, product design, etc. what would you think how much theproduct price has an impact on sales in terms of percentage?