1 As a condition of employment Fashion Industries applicants

1) As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 220 applicants 14 failed the test. Develop a 99% confidence interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that more than 10 percent of the applicants are now failing the test?

2) As part of their business promotional package, the Milwaukee Chamber of commerce would like an estimate of the mean cost per month to lease a one bedroom apartment. A random sample of 40 apartments currently available for lease showed the mean cost per month was $323. The standard deviation of the sample was $25. Develop a 98% confidence interval for the population mean. Would it be reasonable to conclude that the population mean is $350 per month?

3) John kept careful records of the fuel efficiency of his new car. After the first nine times he filled up the tank, he found that the mean was 23.4 per gallon (mpg) with a sample standard deviation of 0.9 mpg. Compute a 95% confidence interval for his mpg.

4) Many retail stores offer their own credit cards. At the time of the credit application the customer is given a 10 percent discount on the purchase. The time required for the credit application process follows a uniform distribution with the times ranging from 4 minutes to 10 minutes.

a. What is the mean time for the application process?

b. What is the standard deviation of the process time?
c. What is the likelihood a particular application will take less than 6 minutes?
d. What is the likelihood an application will take more than 5 minutes?

5) A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 P.M. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find:

a. No customers are waiting?

b. Four customers are waiting?

c. Four or fewer are waiting?

d. Four or more are waiting?

6) Recent difficult economic times have caused an increase in the foreclosure rate of home mortgages. Statistics from the Penn Bank and Trust Company show their monthly foreclosure rate is now one loan out of every 136 loans. Last month the bank approved 300 loans.

a. How many foreclosures would you expect the bank to have last month?

b. What is the probability of exactly two foreclosures?

c. What is the probability of at least one foreclosure?

7) A professor of statistics feels that the performance level of students has gone down recently. In the pass, final exam scores used to have a mean of 75 and standard deviation Last semester the average score was on the final exam was 71 for a class of 31 students. Does this really justify the professor’s concern?

8) It is reported that the average amount of mortgage a home owner in Sussex country carries is $111,000. An executive of a national mortgage company conducts a survey of 40 mortgages and finds the mean amount to be $108000 with a standard deviation of $12000. What should she conclude about the report at a significant level of 5%?

9) The workers at an upstate country rubbish removal company started to demand wage increase, citing the unprecedented increase in the amount of garbage thrown out by the country\'s residents. It is desired to conduct an investigation to determine if the workers’ claims is true. Past data indicate that the amounts of garbage generated by the families in the country closely follow a normal distribution with mean 40lbs and standard deviation 12lbs. The investigator picks a random sample of 36 families’ garbage and finds that the average is 46lbs. What should the investigator conclude?

10) The average score on the SSC303 exam is average is 70 and the standard deviation is 4.

a) What is the probability that a student will score between 72 and 80?

b) What is the probability that a student will score 65?

c) What is the probability that a student will score more than 75?

d) What should a student score to be on the top 10%?

Solution

1.

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.063636364          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.01645749          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.042391686          
lower bound = p^ - z(alpha/2) * sp =   0.021244678          
upper bound = p^ + z(alpha/2) * sp =    0.106028049          
              
Thus, the confidence interval is              
              
(   0.021244678   ,   0.106028049   ) [ANSWER]

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As not all of this interval is greater than 0.10, then no, we it is not reasonable to conclude that more than 10 percent of the applicants are now failing the test. [ANSWER]

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