In May 2025
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Question 3 [25]
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?
Question 2 [25]
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?
Question 1 [25]
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.
Direction: Answer the given problem.
The Guidance Counselor of your school claims that the Grade 11 students spend an average of 11.28 hours in a week doing performance tasks with standard deviation of 1.64. Your adviser thinks that students spend more time in doing performance tasks, so he decided to conduct his own research. He used a sample of 46 Grade 11 students and obtained a mean of 11.83. Is there enough evidence at 0.05 level of significance that the students spend 11.28 hours in a week doing performance tasks?
Cite five (5) research questions used in real life and formulate your null and alternative hypotheses.
Example: Is it true that turmeric can prevent viruses?
Ho: Drinking turmeric cannot prevent viruses.
Ha: Drinking turmeric can prevent viruses.
Sketch a normal curve that has a mean of 60 and a standard deviation of 12. On the same x-axis, sketch another normal curve that has a mean of 90 and a standard deviation of 6. Describe the two normal curves.
Random samples of size 3 are taken from a population of the numbers 3, 4, 5, 6, 7, 8, and 9.
1. How many samples are possible?
2. Construct the sampling distribution of the sample means.
The number of grams of carbohydrates contained in a 1-ounce servings of randomly selected chocolates and non-chocolate candy is listed below. Is there sufficient evidence to conclude that the difference in the carbohydrates content is significant?
Chocolate
29 25 17 36 41 25 32 29 38 34 24 27 29 31 23 42
Non-chocolate
41 41 37 29 30 38 39 10 29 55 29 34 32 38 53 36
Consider an experiment of tossing an unbiased coin three times. What is the probability of obtaining four heads?
Select one:
a. 1
b. ½
c. 0
d. ¼
In which of the approaches to probability are personal conviction, belief and experience are employed to express probability of an event occurring?
Select one:
a. Subjective
b. Standard
c. Experimental
d. Relative frequency
