Search & Filtering
1. Find the range, the standard deviation, and the variance for the given samples. Round noninteger results to the nearest tenth.
a. 1, 2, 5, 7, 8, 19, 22
b. 3, 4, 7, 11, 12, 12, 15, 16
c. 2.1, 3.0, 1.9, 1.5, 4.8
d. 5.2, 11.7, 19.1, 3.7, 8.2, 16.3
2. A mountain climber plans to buy some rope to use as a lifeline. Which of the following would
be the better choice? Explain why you think your choice is the better choice.
Rope A: Mean breaking strength: 500 lb; standard deviation of 100 lb
Rope B: Mean breaking strength: 500 lb; standard deviation of 10 lb
3. Evaluate the accuracy of the following statement: When the mean of a data set is large, the
standard deviation will be large. Explain.
III. Answer the following problems comprehensively.
2. A professor grades students on 5 tests, a project, and a final examination. Each test
counts as 10% of the course grade. The project counts as 20% of the course grade. The
final examination counts as 30% of the course grade. Samantha has test scores of 70,
65, 82, 94, and 85. Samantha’s project score is 92. Her final examination score is 80.
Use the weighted mean formula to find Samantha’s average for the course. Hint: The
sum of all the weights is 100%.
3. A salesperson records the following daily expenditures during a 10-day trip. ₱185.34
₱234.55, ₱211.86, ₱147.65, ₱205.60, ₱216.74, ₱1345.75, ₱184.16, ₱320.45, ₱88.12.
In your opinion, does the mean or the median of the expenditures best represent the
salesperson’s average daily expenditure? Explain your reasoning.
4. If exactly one number in a set of data is changed, will this necessarily change the mean
of the set? Explain.
III. Answer the following problems comprehensively.
2. A professor grades students on 5 tests, a project, and a final examination. Each test
counts as 10% of the course grade. The project counts as 20% of the course grade. The
final examination counts as 30% of the course grade. Samantha has test scores of 70,
65, 82, 94, and 85. Samantha’s project score is 92. Her final examination score is 80.
Use the weighted mean formula to find Samantha’s average for the course. Hint: The
sum of all the weights is 100%.
3. A salesperson records the following daily expenditures during a 10-day trip. ₱185.34
₱234.55, ₱211.86, ₱147.65, ₱205.60, ₱216.74, ₱1345.75, ₱184.16, ₱320.45, ₱88.12.
In your opinion, does the mean or the median of the expenditures best represent the
salesperson’s average daily expenditure? Explain your reasoning.
4. If exactly one number in a set of data is changed, will this necessarily change the mean
of the set? Explain.
1. Find the range, the standard deviation, and the variance for the given samples. Round noninteger results to the nearest tenth.
a. 1, 2, 5, 7, 8, 19, 22
b. 3, 4, 7, 11, 12, 12, 15, 16
c. 2.1, 3.0, 1.9, 1.5, 4.8
d. 5.2, 11.7, 19.1, 3.7, 8.2, 16.3
2. A mountain climber plans to buy some rope to use as a lifeline. Which of the following would
be the better choice? Explain why you think your choice is the better choice.
Rope A: Mean breaking strength: 500 lb; standard deviation of 100 lb
Rope B: Mean breaking strength: 500 lb; standard deviation of 10 lb
3. Evaluate the accuracy of the following statement: When the mean of a data set is large, the
standard deviation will be large. Explain.
1. Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier?
2. Two players A and B are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that A and B give the correct answer areαandβrespectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if
a) A answers the first question,
b) B answers the first question.
Suppose two coins are tossed. Let Y be the random variable representing the number of tails occur. Find the values of the random variable.
A factory manufacturing light emitting diode LED bulbs claims that their light bulbs last
for 50,000 hours on the average. To confirm if this is valid, a quality control manager obtained a
sample of 50 LED light bulbs and got a mean lifespan of 40,000 hours. The standard deviation of
the manufacturing process is 1000 hours.
1. What is the best point estimate for the true mean life span of the LED light bulbs
manufactured by this factory.
2. What is the standard error of this point estimate?
3. What is the margin of error of this point estimate?
4. Construct a 95% confidence interval of the true mean life span of LED light bulbs
manufactured by this factory.
5. Do you think that the claim of the manufacturer is valid? Explain.
6. If you want to be 99% confident that the point estimate is at most 100 hours from the true
mean life span, how many light bulbs should be included in the sample?
1.2 It has been established that completion of construction projects can be delayed because of
unfavourable weather conditions. The probabilities are 0.6 that there will be unfavourable
weather, and 0.85 that the construction project will be completed on time if the weather is
favourable and 0.35 that the construction project will be completed on time if there is
unfavourable weather.
Required:
What is the probability that the construction project will not be completed on time? (10)
Question II [25]
car dealer has established that 40% of his potential customers prefer single cab cars while
60% prefer double cab cars. From a recent survey among his existing clients, he obtained
additional information which indicates that 15% of clients who bought single cab cars prefer
air conditioning while 65% of clients who bought double cars prefer air conditioning.
a) What is the probability that a client who bought a single cab does not prefer air
conditioning? (5)
b) What is the probability that a client prefers a double cab with air conditioning? (10)
Question III [25]
Suppose that a Covid-19 testing centre receives two phones calls, on average, per minute
concerning test results.
Required:
a) What are the conditions for this experiment to be considered a Poisson experiment?
Motivate. (4)
b) What is the expected number of phone calls regarding test results per hour? (2)
c) What is the probability that more zero but less than four phone calls regarding test results
are received in any given period of two minutes? (9)
d) What is the probability that more than one phone calls regarding test results are received
in any given period of three minutes? (7)
e) What is the probability that no phone calls regarding test results are received in any given
period of one minute?
