Statistics and Probability Answers

An insurance company insured 1000 scooter drivers, 3000 car drivers and 6000 truck drivers. The

probabilities that the scooter, car and truck drivers meet with an accident are 0.2, 0.04 and meets

with an accident. What is the probability that he is a car drivers ?

To estimate the average number of customers entering and buying at the supermarket, the supervisor of that supermarket estimated the number of customers visiting every 5 minutes. She randomly selects 5-min intervals and counts the number of arrivals at the supermarket. The figure 58, 32, 41, 56, 80, 45, 29, 32, and 78 were obtained and tallied. The analysis assume that the number of arrivals is normally distributed. What is the 95% confidence interval to have an estimation of the mean value for all 5-min intervals?

A random sample of 50 students is chosen from a large population whose diastolic blood pressures has a standard deviation of 5mm Hg. If the 50 students gave a mean pressure of 80 mm Hg, compute the 88.12% confidence interval of the mean of the diastolic pressures of all students.

1. To estimate the average number of customers entering and buying at the supermarket, the supervisor of that supermarket estimated the number of customers visiting every 5 minutes. She randomly selects 5-min intervals and counts the number of arrivals at the supermarket. The figure 58, 32, 41, 56, 80, 45, 29, 32, and 78 were obtained and tallied. The analysis assume that the number of arrivals is normally distributed. Based on these data, compute a 95% confidence interval to have an estimation of the mean value for all 5-min intervals.

A financial analyst wanted to determine the mean annual return on mutual funds. A random sample of 60 returns shows a mean of 12%. If the population standard deviation is assumed to be 4%, estimate with 95% confidence the mean annual return on all mutual funds.

The following table is a frequency table of the scores obtained in a competition. Use the table answer the questions below.

Classes

Frequency(f)

10 - 13 4

13 - 16 6

16 - 19 12

19 - 22 14

22 - 25 4

Total 40

a. Find the mean, median and mode of the score. [2,2,2]

b. Find the range, variance, and standard deviation. [1,3,1]

c. Find the coefficient of variation. [2]

d. Compute the interquartile range.

A new test for COVID-19 has been developed. It gives either a positive or a

negative result. Experiments have been carried out on the usefulness of this

test, on people known to have COVID-19 and people known not to have

COVID-19. The results of these experiments were:



if the tested person has COVID-19, there is a 0.90 probability that the

test will be positive;



if the tested person does not have COVID-19, there is a 0.95 probability

that the test will be negative.

Suppose that 8% of the people to be tested do in fact have COVID-19.

(i)

Work out the probability that a randomly selected person will test positive

(ii)

suppose that a randomly selected person tests positive. Work out the

probability that he or she actually has COVID-19.

(iii)

Suppose that a randomly selected person tests negative. Work out the

probability that he or she actually has COVID-19.

Because a new medical procedure has been shown to be effective in the early detection of an illness, a medical screening of the population has been proposed. The probability that the test correctly identifies someone with the illness as positive is 0.99, and the probability that the test correctly identifies someone without the illness as negative is 0.95. The incidence of the illness in the general population is 0.0001.

Hint: You may use a probability diagram or tree diagram to aid you in solving the problem.

Let D= Presence of the disease in the population

A= absence of the disease in the population

N= Negative results

P= positive results

a. What is the probability that the test will diagnose a person as having the illness? [4]

b. You take the test, and the result is positive. What is the probability that you have the illness?

UESTION TWO

The time it takes a randomly selected employee to perform a task is mean value of 120 seconds and standard deviation of 20 seconds.

INCOME-y 28

31

34

30 35 158

            Calculate the probability that a randomly selected employee will complete:

2.1.1 The task within 100 to 130 sec (5)

2.1.2 In more than 75sec