Statistics and Probability Answers

4. The mean expenditure per customer at a department store is Birr 85 with standard deviation of Birr 9. If a random sample of 40 customers is taken, what is the probability that the sample average expenditure per customer will be
a) Birr 87 or more
b) Less than Birr 82
c) Between Birr 83 and 85

The average grade/mark of all college students is 70 with standard deviation of 20. If a random sample of 49 students is taken, what is the probability that the sample average grade/mark is
a) At least 65
b) Less than 78
c) Between 65 and 72

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Human Resource Consulting (HRC) surveyed a random sample of 76 Twin Cities construction companies to find information on the costs of their health care plans. One of the items being tracked is the annual deductible that employees must pay. The Minnesota Department of Labor reports that historically the mean deductible amount per employee is $503 with a standard deviation of $115. (Round your z value to 2 decimal places and final answers to 4 decimal places. Leave no cells—blankbe certain to enter "0" if required.)



Compute the standard error of the sample mean for HRC.

A package of 6 fuses are tested where the probability an individual fuse is defective is 0.05 that is 5% of all fuses manufactured are defective . (a) . What is tue probability at least one fuse will be defective ? (b) . What is tue probability that more than one fuse will be defective given that at level one is defective ?

Two soil samples consisting of 21 and 9 observations have variances of 18 and 8 respectively. Test the hypothesis that the first population variance is greater than the second at (a) 0.05 and (b) 0.01 levels of significance. (c) Repeat the same test If the two samples consist of 60 and 120 observations.

A financial analyst has found out that policyholders are four times as likely to file two
claims as to file four claims. If the number of claims filed has a posson distribution,
what is the variance of the number of claims filed.

A computer manager needs to know how efficiency of her new computer program depends
on the size of incoming data. Efficiency will be measured by the number of processed
requests per hour. Applying the program to data sets of different sizes, she obtains the
following results,
Data size (gigabytes) 6 7 7 8 10 10 15
Processed requests 40 55 50 41 17 26 16
i. Draw the scatterplot for the data. Be sure to label your axes.
ii. Is there any correlation between the processing request and the size of incoming data?
What is the correlation coefficient?
iii. By what percentage is the processing time dependent on the size of incoming data?
iv. Compute a least square regression line for regressing processing request on the size of
incoming data.
v. Use your regression equation to predict the processing request for an incoming data
of size 17.0 gigabytes
vi. Is the slope statistically significant at α = 5% ?

Suppose that we want to test the claim that the mean of a population is greater than 20. Also suppose that the population standard deviation is known to be 7. A sample of 49 measurements reveals a mean of 22. What is the value of the test statistic?

3. The lifetime of a machine is continuous on the interval (0, 40) with probability density
function f, where f(t) is proportional to (t + 10)) 2
, and t is the lifetime in years.
Calculate the probability that the lifetime of the machine part is less than 10 years.
Hint: Show that f(t) is legitimate and find the proportionality constant

A financial analyst has found out that policyholders are four times as likely to file two
claims as to file four claims. If the number of claims filed has a posson distribution,
what is the variance of the number of claims filed.