Topic: Probability

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QTB – Nov 2014 – L1 – SA – Q3 – Probability

Determines the probability that daily sales exceed a specified value, given a normal distribution with known mean and standard deviation.

Question

The daily sales figures of a supermarket follow a normal distribution with a mean of N60,000 and a standard deviation of N14,000. Find the probability that the sales figure of a certain day exceeds N46,000.
A. 0.1587
B. 0.1590
C. 0.8413
D. 0.8415
E. 0.8423

Answer

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Tags: Normal distribution, Probability, Sales Data
Level: Level 1

Topic: Probability
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q2 – Probability

Determines the probability that a customer does not receive a mutilated note from the cashiers.

Question

The following tree diagram shows the scenario with two paying cashiers (C1 and C2) at a Microfinance Bank where M represents mutilated notes and N represents new notes:

he probability that a customer of the bank does not receive a mutilated note is:
A. 0.1125
B. 0.8725
C. 0.8875
D. 0.8525
E. 0.8850

Answer

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Tags: Cashiers, Mutilated Notes, Probability, Tree Diagram

Topic: Probability
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q1 – Probability

Determines the correct definition of mutually exclusive events.

Question

Two events are said to be mutually exclusive if
A. The occurrence (or non-occurrence) of one event does not affect the occurrence (or non-occurrence) of the other event
B. Both events can occur simultaneously
C. The occurrence of one event precludes the occurrence of the other event
D. Both are impossible events

Answer

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Tags: Mutually Exclusive Events, Probability, Statistics
Level: Level 1

Topic: Probability
Series: NOV 2014

QT – May 2016 – L1 – Q4 – Probability

Determine percentages of receipts using normal distribution and calculate mean and standard deviation based on given conditions.

Question

a) Receipts at a particular depot have amounts which follow the Normal distribution with a mean of GH¢103.60 and a standard deviation of GH¢8.75.

Required:
i) Determine the percentage of receipts over GH¢120.05.
ii) Determine the percentage of receipts below GH¢92.75.
iii) Determine the percentage of receipts between GH¢83.65 and GH¢117.60.
iv) Determine the receipts amount such that approximately 25 percent of receipts are greater.
v) Above what amount will 90 percent of receipts lie?

b) If 10.56 percent of receipts have an amount above GH¢110.05 and 4.01 percent of receipts have an amount above GH¢120.05.

Required:
Calculate the mean and standard deviation of the receipts assuming that they are normally distributed.

Answer

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Tags: Mean, Normal distribution, Probability, Receipts, Standard Deviation, Z-scores
Level: Level 1

Topic: Probability
Series: MAY 2016

QT – May 2016 – L1 – Q3 – Probability

Calculate the probabilities of various outcomes in a card drawing scenario, including conditional probability based on drawing a red card.

Question

a) If from a normal pack of 52 cards, consisting of four suites each of 13 cards, one card is randomly selected:

Required:

Calculate the probabilities of selecting the following:

i) An ace
ii) A club
iii) An ace or a club
iv) The ace of clubs
v) A picture card (i.e. a jack, queen or king)
vi) A red card
vii) A red king
viii) A red picture card

b) Given that a card selected is red, calculate the probability that it is a picture card.

Answer

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Tags: Card Shuffle, Conditional Probability, Mutually Exclusive Events, Probability
Level: Level 1

Topic: Probability
Series: MAY 2016

QT – Nov 2017 – L1 – Q5 – Probability

Use the normal distribution to compute probabilities related to loan default amounts.

Question

The distribution of the total loan amounts defaulted by customers of a bank annually is approximated by a normal distribution. The average default amount is GH¢1.50 million, and the standard deviation is GH¢0.50 million.

Required:
a) Determine the probability that the total loan amount defaulted exceeds GH¢1.50 million. (3 marks)
b) Determine the probability that the total loan amount defaulted is between GH¢0.86 million and GH¢0.90 million. (4 marks)
c) Determine the probability that the total amount defaulted is at most GH¢2 million. (4 marks)
d) Determine the amount to be allowed per annum for loan defaults if 1% of actual defaults exceed this amount. (3 marks)
e) Determine the lower quartile of the distribution of total loan amounts defaulted. (3 marks)
f) Determine the upper quartile of the distribution of total loan amounts defaulted. (3 marks)
(Total: 20 marks)

Answer

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Tags: Loan Defaults, Normal distribution, Probability
Level: Level 1

Topic: Probability
Series: NOV 2017

QT – May 2019 – L1 – Q6b – Probability

Calculate probabilities based on student survey data regarding their favorite sports.

Question

A survey of The Institute of Chartered Accountants (Ghana) students asked the question: “What is your favourite sport?” The results are summarized below:

Level	Football	Boxing	Hockey	Total
1	68	41	46	155
2	84	56	70	210
3	59	74	47	180
Total	211	171	163	545

Required: i) What is the probability of selecting a student whose favourite sport is boxing? (2 marks)

ii) What is the probability of selecting a Level 1 student? (2 marks)

iii) If the student selected is a Level 2 student, what is the probability that the student prefers hockey? (3 marks)

iv) If the student selected is a Level 2 student, what is the probability that the student prefers football or hockey? (3 marks)

v) If the student selected prefers football, what is the probability that the student is a Level 1 student? (3 marks)

vi) If the student selected is a Level 3 student, what is the probability that the student prefers football, boxing, or hockey? (3 marks)

Answer

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Tags: Conditional Probability, Probability, Probability Calculation, Survey Data
Level: Level 1

Topic: Probability
Series: MAY 2019

QT – May 2019 – L1 – Q6a – Probability

Define collectively exhaustive events and complement of an event in probability theory.

Question

Define the following terms in probability theory:

i) Collectively exhaustive events (2 marks)
ii) The complement of an event (2 marks)

Answer

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Tags: Collectively Exhaustive Events, Complement of Event, Probability Theory
Level: Level 1

Topic: Probability
Series: MAY 2019

QT – May 2019 – L1 – Q4b – Probability

Solve problems involving normal distribution, life spans, and warranty calculation using Z-scores.

Question

CarJoy Manufacturing Company produces electronic components that have life spans normally distributed with mean $μ$ hours and standard deviation hours. Only 1% of the components have a life span less than 3,500 hours and 2.5% have a life span greater than 5,500 hours.

Required:
i) By standardizing the values of $X$ to the standard normal values, obtain TWO (2) linear equations in $μ$ and $σ$ . (4 marks)

ii) Using an appropriate method of solving simultaneous equations, determine the value of $μ$ and $σ$ in (i) above. (4 marks)

iii) Determine the proportion of electronic components with life spans between 4,120.50 hours and 5,052.45 hours. (4 marks)

iv) If the company gives a warranty of 4,000 hours on the components, find the percentage of components the company is expected to replace under the warranty. (4 marks)

Answer

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Tags: Normal distribution, Probability, Standard Deviation, Warranty Calculation, Z-scores
Level: Level 1

Topic: Probability
Series: MAY 2019

QT – May 2019 – L1 – Q4a – Probability

Sketch the normal distribution curve showing the mean, median, and mode.

Question

The continuous random variable is normally distributed with mean $μ$ and variance $σ^{2}$ .

Required:
Sketch the distribution of $X$ and indicate on your sketch the mean, median, and mode. (4 marks)

Answer

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Tags: Mean, Median, Mode, Normal distribution, Probability
Level: Level 1

Topic: Probability
Series: MAY 2019

QTB – Nov 2014 – L1 – SA – Q3 – Probability

Determines the probability that daily sales exceed a specified value, given a normal distribution with known mean and standard deviation.

Question

Answer

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Tags: Normal distribution, Probability, Sales Data
Level: Level 1

Topic: Probability
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q2 – Probability

Determines the probability that a customer does not receive a mutilated note from the cashiers.

Question

The following tree diagram shows the scenario with two paying cashiers (C1 and C2) at a Microfinance Bank where M represents mutilated notes and N represents new notes:

he probability that a customer of the bank does not receive a mutilated note is:
A. 0.1125
B. 0.8725
C. 0.8875
D. 0.8525
E. 0.8850

Answer

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Tags: Cashiers, Mutilated Notes, Probability, Tree Diagram

Topic: Probability
Series: NOV 2014

QTB – Nov 2014 – L1 – SA – Q1 – Probability

Determines the correct definition of mutually exclusive events.

Question

Answer

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Tags: Mutually Exclusive Events, Probability, Statistics
Level: Level 1

Topic: Probability
Series: NOV 2014

QT – May 2016 – L1 – Q4 – Probability

Determine percentages of receipts using normal distribution and calculate mean and standard deviation based on given conditions.

Question

a) Receipts at a particular depot have amounts which follow the Normal distribution with a mean of GH¢103.60 and a standard deviation of GH¢8.75.

b) If 10.56 percent of receipts have an amount above GH¢110.05 and 4.01 percent of receipts have an amount above GH¢120.05.

Required:
Calculate the mean and standard deviation of the receipts assuming that they are normally distributed.

Answer

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Tags: Mean, Normal distribution, Probability, Receipts, Standard Deviation, Z-scores
Level: Level 1

Topic: Probability
Series: MAY 2016

QT – May 2016 – L1 – Q3 – Probability

Calculate the probabilities of various outcomes in a card drawing scenario, including conditional probability based on drawing a red card.

Question

a) If from a normal pack of 52 cards, consisting of four suites each of 13 cards, one card is randomly selected:

Required:

Calculate the probabilities of selecting the following:

i) An ace
ii) A club
iii) An ace or a club
iv) The ace of clubs
v) A picture card (i.e. a jack, queen or king)
vi) A red card
vii) A red king
viii) A red picture card

b) Given that a card selected is red, calculate the probability that it is a picture card.

Answer

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Tags: Card Shuffle, Conditional Probability, Mutually Exclusive Events, Probability
Level: Level 1

Topic: Probability
Series: MAY 2016

QT – Nov 2017 – L1 – Q5 – Probability

Use the normal distribution to compute probabilities related to loan default amounts.

Question

Answer

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Tags: Loan Defaults, Normal distribution, Probability
Level: Level 1

Topic: Probability
Series: NOV 2017

QT – May 2019 – L1 – Q6b – Probability

Calculate probabilities based on student survey data regarding their favorite sports.

Question

A survey of The Institute of Chartered Accountants (Ghana) students asked the question: “What is your favourite sport?” The results are summarized below:

Level	Football	Boxing	Hockey	Total
1	68	41	46	155
2	84	56	70	210
3	59	74	47	180
Total	211	171	163	545

Required: i) What is the probability of selecting a student whose favourite sport is boxing? (2 marks)

ii) What is the probability of selecting a Level 1 student? (2 marks)

iii) If the student selected is a Level 2 student, what is the probability that the student prefers hockey? (3 marks)

iv) If the student selected is a Level 2 student, what is the probability that the student prefers football or hockey? (3 marks)

v) If the student selected prefers football, what is the probability that the student is a Level 1 student? (3 marks)

vi) If the student selected is a Level 3 student, what is the probability that the student prefers football, boxing, or hockey? (3 marks)

Answer

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Tags: Conditional Probability, Probability, Probability Calculation, Survey Data
Level: Level 1

Topic: Probability
Series: MAY 2019

QT – May 2019 – L1 – Q6a – Probability

Define collectively exhaustive events and complement of an event in probability theory.

Question

Define the following terms in probability theory:

i) Collectively exhaustive events (2 marks)
ii) The complement of an event (2 marks)

Answer

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Tags: Collectively Exhaustive Events, Complement of Event, Probability Theory
Level: Level 1

Topic: Probability
Series: MAY 2019

QT – May 2019 – L1 – Q4b – Probability

Solve problems involving normal distribution, life spans, and warranty calculation using Z-scores.

Question

Required:
i) By standardizing the values of $X$ to the standard normal values, obtain TWO (2) linear equations in $μ$ and $σ$ . (4 marks)

ii) Using an appropriate method of solving simultaneous equations, determine the value of $μ$ and $σ$ in (i) above. (4 marks)

iii) Determine the proportion of electronic components with life spans between 4,120.50 hours and 5,052.45 hours. (4 marks)

iv) If the company gives a warranty of 4,000 hours on the components, find the percentage of components the company is expected to replace under the warranty. (4 marks)

Answer

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Tags: Normal distribution, Probability, Standard Deviation, Warranty Calculation, Z-scores
Level: Level 1

Topic: Probability
Series: MAY 2019

QT – May 2019 – L1 – Q4a – Probability

Sketch the normal distribution curve showing the mean, median, and mode.

Question

The continuous random variable is normally distributed with mean $μ$ and variance $σ^{2}$ .

Required:
Sketch the distribution of $X$ and indicate on your sketch the mean, median, and mode. (4 marks)

Answer

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Tags: Mean, Median, Mode, Normal distribution, Probability
Level: Level 1

Topic: Probability
Series: MAY 2019

Topic: Probability

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QTB – Nov 2014 – L1 – SA – Q3 – Probability

Determines the probability that daily sales exceed a specified value, given a normal distribution with known mean and standard deviation.

QTB – Nov 2014 – L1 – SA – Q2 – Probability

Determines the probability that a customer does not receive a mutilated note from the cashiers.

QTB – Nov 2014 – L1 – SA – Q1 – Probability

Determines the correct definition of mutually exclusive events.

QT – May 2016 – L1 – Q4 – Probability

Determine percentages of receipts using normal distribution and calculate mean and standard deviation based on given conditions.

QT – May 2016 – L1 – Q3 – Probability

Calculate the probabilities of various outcomes in a card drawing scenario, including conditional probability based on drawing a red card.

QT – Nov 2017 – L1 – Q5 – Probability

Use the normal distribution to compute probabilities related to loan default amounts.

QT – May 2019 – L1 – Q6b – Probability

Calculate probabilities based on student survey data regarding their favorite sports.

QT – May 2019 – L1 – Q6a – Probability

Define collectively exhaustive events and complement of an event in probability theory.

QT – May 2019 – L1 – Q4b – Probability

Solve problems involving normal distribution, life spans, and warranty calculation using Z-scores.

QT – May 2019 – L1 – Q4a – Probability

Sketch the normal distribution curve showing the mean, median, and mode.

QTB – Nov 2014 – L1 – SA – Q3 – Probability

Determines the probability that daily sales exceed a specified value, given a normal distribution with known mean and standard deviation.

QTB – Nov 2014 – L1 – SA – Q2 – Probability

Determines the probability that a customer does not receive a mutilated note from the cashiers.

QTB – Nov 2014 – L1 – SA – Q1 – Probability

Determines the correct definition of mutually exclusive events.

QT – May 2016 – L1 – Q4 – Probability

Determine percentages of receipts using normal distribution and calculate mean and standard deviation based on given conditions.

QT – May 2016 – L1 – Q3 – Probability

Calculate the probabilities of various outcomes in a card drawing scenario, including conditional probability based on drawing a red card.

QT – Nov 2017 – L1 – Q5 – Probability

Use the normal distribution to compute probabilities related to loan default amounts.

QT – May 2019 – L1 – Q6b – Probability

Calculate probabilities based on student survey data regarding their favorite sports.

QT – May 2019 – L1 – Q6a – Probability

Define collectively exhaustive events and complement of an event in probability theory.

QT – May 2019 – L1 – Q4b – Probability

Solve problems involving normal distribution, life spans, and warranty calculation using Z-scores.

QT – May 2019 – L1 – Q4a – Probability

Sketch the normal distribution curve showing the mean, median, and mode.

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