MAT 161Name ______
Final Review
Chapter 1 -3
1.The following data give the weight (in pounds) lost by 14 new members of a health club at the end of their first two months of membership.
612891115101281 14121014
a. What type of variable is it? (discrete, continuous or qualitative)
b. Find the sample mean.
c. Find the sample standard deviation.
d. Find the median.
e. Find the mode.
f. Find the range.
g. Find the 79th percentile.
2. The following data give the number of computer keyboards assembled at the Twentieth Century Electronics Company for a sample of 25 days.
21324341523851504243313331
363342405437242730293238
a. Construct an ordered stem and leaf plot of these ages.
b. Find the 5-number summary of the data.
c. Draw a box and whisker diagram for this data on the grid below.
Chapter 4
3.The following table lists the midterms and final exam scores for eight students in a statistics class.
Midterm6885817677936976
Final7587787684917583
a. Find linear correlation for this data. Explain what this means.
b. Find the linear regression equation or equation of the line of best fit for this data.
c. Find the coefficient of determination for this data. Explain what it means.
Chapter 5
- A box contains a total of 100 cassettes that were manufactured on two machines. Of them, 59 were manufactured on Machine I. Of the total cassettes, 15 are defective. Of the 59 cassettes that were manufactured on Machine I, 10 are defective.
Let D: a randomly selected cassette is defective
Let A: a randomly selected cassette was manufacture on Machine I
DefectiveGood
(D)(G)Total
Machine I (A)1049 59
Machine II (B) 536 41
Total 1585100
Find the following probabilities.
a. P(A)
b. P(D)
c. P(D and A)
d.P(A or D)
e.P(D | A)
f. Are A and D mutually exclusive? Explain your answer.
g. Are A and D independent? Explain your answer.
Chapter 6
5.An arsenal contains several identical boxes of ammunition. If the number of defective bullets per box has the following distribution, find the mean and standard deviation for x.
xP(x)
00.90
10.07
20.03
a. Find .
b. Find .
6. A doctor knows from experience that 10% of the patients to whom he gives a certain drug will have undesirable side effects. Find the probabilities that among the ten patients to whom he gives the drug,
a. exactly three will have the undesirable side effects.
b.exactly three will have NOT the undesirable side effects.
c. none of the patients will have the undesirable side effects.
e. at least two patients will have the undesirable side effects.
f. at most one will have the undesirable side effects.
7.Given the probability that a patient’s full recovery from a certain disease is 0.4, find each of the following.
a. The probability that exactly one of a set of six patients will recover.
b.Calculate the mean number of patients that will recover for each set of six patients under the above conditions.
c. Calculate the standard deviation of the number of patients that recover for each group of six patients.
Chapter 7
8. Draw the curve, label it and then find P(z>-1.52).
9. Draw the curve, label it and then find P(- 1.5 < z < 2.0).
10.In a bowling league, the bowling averages are normally distributed with a mean of 155.6 and a standard deviation of 7.9.
a. What percentage of the bowlers in this league have an average below 150?
b.If a bowler is selected at random from this league, what is the probability that his average is between 150 and 170?
Chapter 8
11.A sample of size 16 is drawn from a population where = 26 and = 4.5. Find the probability that the sample mean is between 24 and 28. (HINT: Sample size is given so be sure to use it.)
12. An aircraft strobe light is designed so that the times between flashes have a mean of 10.15 s and a standard deviation of 0.40 s. A sample of 50 times is randomly selected. Find the probability that the sample mean is greater than 10.00 s.
Chapter 9
13.Oranges are selected at random from a large shipment that just arrived. The sample was taken to estimate the size(circumference, in inches) of the oranges. A sample of 100 oranges was taken and the sample mean was 8.78 inches with a standard deviation of 0.710. Find the 98% confidence interval for . Explain what it means.
14. A NY state official intends to use the mean of a random sample of 500 fourth graders to estimate the mean score of all fourth graders in the state on the ELA exam. The standard deviation of the test was 12.4.The sampled students’ averaged 58.6 on the test, construct a 95% confidence interval for the mean score of all fourth graders on this test.
15.On a standard IQ test, is 15. How many random IQ scores must be obtained if we want to find the true population mean (with an allowable error of 0.5) and we want 99% confidence in the results?
16.A high tech company wants to estimate the mean number of years of college education its employees have completed. A good estimate of the standard deviation for the number of years is 1.0. How large a sample needs to be taken to estimate to within 0.5 of a year with 95% confidence?
Chapter 10
17.A random sample of 100 students was taken to test the claim that the mean amount of time college students spend watching TV per week is greater than 14.5 hours. The resulting values yielded a mean of 16.3 hours. Complete using the p-value approach the hypothesis test using a = 5.2 and = 0.02.
Hypothesis:Ho:
H1:
Test type:
Data Entered:
Test* found:
Decision:
Conclusion:
18.Test the claim that a certain x-ray machine gives radiation dosages with a mean below 5.00 milliroentgens. Sample data consists of 36 observations with a mean of 4.13 milliroentgens and a standard deviation of 1.91 milliroentgens. Use a 0.01 level of significance. Complete the hypothesis test using the p-value approach.
Hypothesis:Ho:
H1:
Test type:
Data Entered:
Test* found:
Decision:
Conclusion:
19. In a large cherry orchard the average yield has been 4.35 tons per acre for the last several years. A new fertilizer was tested on 15 randomly selected one-acre plots. The yields from these plots follow:
3.565.004.884.933.924.255.125.134.794.45
5.354.813.484.454.72
At the 0.05 level of significance, do we have sufficient evidence to claim that there was a significant increase in production? Assume yield per acre is normally distributed.
Hypothesis:Ho:
H1:
Test type:
Data Entered:
Test* found:
Decision:
Conclusion :
20.A production process is considered out of control if the produced parts have a mean length different from 27.5 mm or a standard deviation that is greater than 0.5 mm. A sample of 30 parts yields a sample mean of 27.63 mm and a sample standard deviation of 0.87 mm. If we assume part length is a normally distributed variable, does this sample indicate that the process should be adjusted in order to correct the standard deviation of the product? Use = 0.05.
Hypothesis:Ho:
H1:
Test type:
Data Entered:
Test* found:
Decision:
Conclusion