Statistics and Probability Answers

Suppose that a mobile telecommunication company’s helpline receives five calls, on average, per minute.

Required:

a) Discuss the difference between the Binomial probability distribution and the Poisson probability distribution.

b) How many calls does the company expect to receive in a period of 30 minutes?

c) What is the probability that the company will receive at most four calls in a period of 4 minutes?

d) What is the probability that the company will receive at least three calls in a period of 5 minutes?

e) What is the probability that the company will receive between six and nine calls in a period of 2 minutes?

Suppose that the latest census indicates that for every 10 young people available to work only 4 are employed. Suppose a random sample of 20 young graduates is selected.

Required:

a) What is the probability that they are all employed?

b) What is the probability that none of them are employed?

c) What is the probability that at least four are employed?

d) What is the probability that at most fifteen are employed?

e) What is the probability that the number of young graduates who are employed is greater than ten but less than fifteen?

f) What is the expected number of graduates who are not employed?

g) What is the standard deviation for the number of graduates who are not employed? 

In a survey conducted among a random sample of students the following observations were made regarding their gender and learning environment preferences during the COVID-19 pandemic:

168 prefer online learning

202 prefer face to face learning

180 prefer blended learning

34 male students prefer online learning and

70 male students prefer blended learning

106 female students prefer face to face learning

Required:

a) What is the probability that a female student is chosen?

b) What is the probability that a male student prefers face to face learning?

c) What is the probability that a student prefers online or blended learning?

d) If it’s known that the student is female, what is the probability that this student prefers online learning.

e) Using a practical example, explain the difference between mutually exclusive events and independent events.

According to the Civil Code of the Philippines, the marriageable age of Filipinos is 18. A researcher found out that the average age of Filipinos who got married is 23 years old. A random sample of 25 married couples were taken. Is there a reason to believe that the sample is significantly younger that the others in getting married at 1% level of significance? (the output range should be at cell G4)

25, 28, 30, 32, 31, 32, 28, 28, 20, 20, 21, 22, 23, 23, 22, 21, 20, 26, 26, 29, 30, 29, 30, 24, 24

If the ANOVA value (F-value) is 2.12 and the critical value are ±1.96, what is the appropriate decision?

A study claims that on average, male high school students spend at least 3.39 hours a day playing video games with a standard deviation of 2.05 hours. A random sample of 30 teenagers were surveyed and the results showed that these teenagers append 4.12 hours a day playing video games. Calculate the probability of getting a smaller average time.