Search & Filtering
Q.1.2 The time taken to complete a web-based questionnaire is normally distributed, with an average time (μ) of 9 minutes and a standard deviation (σ) of 1.55 minutes. What is the probability that a randomly selected person will take: Q.1.2.1 Between 8 and 8.5 minutes to complete the questionnaire? Interpret your answer. (5) Q.1.2.2 Between 8.75 and 9.75 minutes to complete the questionnaire? Interpret your answer.
A 40-year-old man in the U.S. has a 0.242% risk of dying during the next year . An insurance company charges $260 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar.
The park officials of Kruger Park believe that 50% of the buffaloes in the southern part have tuberculosis.
The characteristic being studied is the occurrence of tuberculosis. A random sample of
100 buffalo is obtained from the southern part of the Kruger Park for which 65 are tested positively
for tuberculosis.
(a) Do the data indicate that the proportion of buffalo in the southern part that have tuberculosis
is greater than assumed? Perform a proper hypothesis test and test at the 5% significance
level. Clearly show how you draw a conclusion when you test this hypothesis, using both
methods, i.e.
critical value approach, and p-value approach
Three men A, B and C agree to meet at the theatre. The man A cannot remember whether they agree to meet at the palace or the queens and tosses a coin to decide which theatre to go to. The man B also tosses a coin to decide between the queens and royalty. The man C tosses a coin to decide whether to go to the palace or not and in this latter case he tosses again to decide between the queens and royal. Find A and B meet, B and C meet, A, B and C all meet, A, B and C all go to different place, and at least two meet.
A liberal organization contacts a simple random sample of 500 Manitoba voters, asking them the following question: “Given the failures of the current Conservative government on health care and education, will you support the Conservative Party in the next election?” 34% of those responding answered yes. Do you suspect an underestimate or overestimate to result from this survey? Why?
Glass Houses Pty has found that the cost of fitting new sliding doors is normally distributed, with an average cost per door of R12 750, and a standard deviation of R1 095. A sample of 105 new windows is randomly selected. Assuming normal distribution: What is the probability that the average cost of fitting the doors in
the sample is less than R13 000? Interpret your answer.
a) A random sample of employee files is drawn revealing an average of 2.8 overtime hours worked per week with a standard deviation of 0.7. The sample size is 500.
(i) What is the standard error of the mean based on this information? (2)
(ii) What is the 98% confidence interval for the number of overtime hours worked? (5)
How would your result be affected if the sample size had been 100?
