Statistics and Probability Answers

The age of the population in Wakanda is shown in the following table in the form of a

grouped frequency distribution.

Age (years) Number (‘000)

0 Under 5 1 375.3

5 under 15 2 750.5

15 under 30 4 514.7

30 under 50 6 137.7

50 under 65 3 821.7

65 under 80 2 045.7

80 under 100 783.2

100 under 110 3.1

Total 21 431.8

Use the data in the table above to estimate for of population in Wakanda the:

BACHELOR OF COMMERCE YEAR 1 – ACADEMIC AND ASSESSMENT CALENDAR - DISTANCE

REGENT BUSINESS SCHOOL (RBS) – JANUARY 2021 15

3.1 median age.

8 Dr. Jones conducted a study examining the relationship between the quality of breakfast and 

academic performance for a sample of n=20 first-grade students. The quality of breakfast was 

determined by interviewing each child’s parents, and academic performance was measured by each 

child’s most recent grades. Is this an example of a correlational or an experimental study? Explain 

your answer. 

Research has shown that 55% of new small medium enterprises (SMEs) are started by graduates, while 45% are started by by non-graduates. It is also known that 70% of the SMEs started by graduates are successful i.e they survive beyond three years while only 10% of those started by non-graduates are successful.

a)If it is known that a new SME is not successful , what is the probability that it was not started by a graduate.

ASSESSMENT: Construct the probability distribution of the situation below:

Two balls are drawn in succession without replacement from an urn containing 5 white balls and 6

black balls. Let B be the random variable representing the number of black balls.

Construct the probability distribution of the random variable B.

Comparing dexterity-test scores of workers on the day shift versus those on the night shift, the production manager of a large electronics plant finds that a sample of 37 workers from the day shift have an average score of 73.1, with a standard deviation of 12.3. For 42 workers from the night shift, the average score was 77.3, with a standard deviation of 8.4. Assuming the population standard deviations are equal, use the 0.05 level of significance in comparing the average scores for the two shifts. Using the appropriate statistical table, what is the most accurate statement we can make about the p-value for this test? Construct and interpret the 95% confidence interval for the difference between the population means.

6 A sample of 40 investment customers serviced by an account manager are found to have had an average of $23,000 in transactions during the past year, with a standard deviation of $8500. A sample of 30 customers serviced by another account manager averaged $28,000 in transactions, with a standard deviation of $11,000. Assuming the population standard deviations are equal, use the 0.05 level of significance in testing whether the population means could be equal for customers serviced by the two account managers. Using the appropriate statistical table, what is the most accurate statement we can make about the p-value for this test? Construct and interpret the 95% confidence interval for the difference between the population means.

According to the Federal Reserve Board, the mean net worth of U.S. households headed by persons 75 years or older is $640,000. Suppose a simple random sample of 50 households in this age group is obtained from a certain region of the United States and is found to have a mean net worth of $615,000, with a standard deviation of $120,000. From these sample results, and using the 0.05 level of significance in a two-tail test, comment on whether the mean net worth for all the region’s households in this age category might not be the same as the mean value reported for their counterparts across the nation.

The service manager of Appliance Universe has recorded the times for a simple random sample of 50 refrigerator service calls taken from last year’s service records. The sample mean and standard deviation were 25 minutes and 10 minutes, respectively. a. Construct and interpret the 95% confidence interval for the mean. b. It’s quite possible that the population of such times is strongly skewed in the positive direction—that is, some jobs, such as compressor replacement, might take 3 or 4 hours. If this were true, would the interval constructed in part (a) still be appropriate? Explain your answer

A robot-controlled joystick may be helpful for many disabled people as electric 

wheelchairs are difficult to maneuver for many disabled people. From a certain location in a room, a wheelchair user will either (1) turn sharply to the left and navigate through a door, (2) proceed straight to the other side of the room, or (3) turn slightly right and stop at a table. Denote these three events as D (for door), S (for other side of the room), and T (for 

table). Based on the previous trips, P(D) = 0.5, P(S) = 0.2, P(T) = 0.3. The wheelchair is 

installed with a robot-controlled joystick. When the user intends to go through the door, he points the joystick straight 30% of the time; when the user intends to go straight, he points the joystick straight 40% of the time; and, when the user intends to go to the table, he points the joystick straight 5% of the time. If the wheelchair user points the joystick straight, what 

is her most likely destination?

is a table, a graph or a formula listing all possible values that a discrete random variable can take on, along with the associated probabilities?