Question Tag: Normal distribution

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QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

Question

Which of the following is NOT TRUE about Normal Distribution?
A. Normal distribution is a frequency distribution.
B. Both tails of the distribution approach but never meet the horizontal axis.
C. It is a probability distribution of a continuous variable that fits many naturally occurring distributions.
D. The exact shape of the normal curve depends on the mean of the distribution.
E. The area under the normal curve represents the probability and totals 1 or 100%.

Answer

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Tags: Business Statistics, Normal distribution, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2017

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 – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

Question

The weights of bags of Pando Yam produced by Swallow Company Limited are normally distributed with a mean of 3,020 grams and a standard deviation of 4 grams.

Required:
i. If a bag is picked at random, what is the probability that it weighs:

Less than 3,012 grams? (4 marks)
ii. Between 3,012 grams and 3,021.6 grams? (6 marks)
Show all the relevant normal distribution diagrams.

Answer

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Tags: Normal distribution, Pando Yam, Probability, Z-scores
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – Nov 2015 – L1 – SA – Q11 – Statistics

This question calculates the area under the normal curve based on the given Z-score.

Question

If the z-score for a normal distribution is 1.89, then the area under the normal curve to the right of z is:

A. 0.02
B. 0.03
C. 0.04
D. 0.47
E. 0.97

Answer

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Tags: Normal distribution, Probability, Z-Score
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – May 2015 – L1 – SB – Q2 – Statistics

Calculating probabilities related to household expenditure on mobile phones.

Question

A research was conducted to know the average monthly household expenditure on mobile phones in DETOTAR Estate.
The research shows the average monthly household expenditure to be N5,200. Assume that the monthly household expenditure on mobile phones in the Estate is normally distributed with a standard deviation of N1,800. Determine the probability of a randomly selected household in DETOTAR Estate if the monthly expenditure on mobile phone is:

a. more than N8,700 (5 Marks)
b. between N2,600 and N9,000 (6 Marks)
c. between N7,600 and N10,200 (6 Marks)
d. less than N8,800 (3 Marks)

Answer

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Tags: Household Expenditure, Normal distribution, Probability
Level: Level 1

Series: MAY 2015

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 – 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 – 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

QT – Nov 2018 – L1 – Q5b – Probability

Solve normal distribution problems related to spending habits of residents in Kojokrom.

Question

In a study commissioned by Ofo Stores, the researcher examined the spending habits of the residents of Kojokrom. He found the spending habits to be normally distributed with a mean of GH¢700 and a standard deviation of GH¢70.

Required:
i) Determine the probability that a resident selected at random spends:

Less than GH¢620 (3 marks)
More than GH¢1,000 (3 marks)
Between GH¢800 and GH¢900 (4 marks)

ii) Calculate the amount:

Above which 80% of the residents will spend in a week (2 marks)
Below which 30% of the residents will spend in a week (2 marks)

Answer

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Tags: Continuous Variables, Normal distribution, Probability, Spending Habits, Statistics
Level: Level 1

Topic: Probability
Series: NOV 2018

QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

Question

Answer

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Tags: Business Statistics, Normal distribution, Probability
Level: Level 1

Topic: Statistics
Series: MAY 2017

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 – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

Question

The weights of bags of Pando Yam produced by Swallow Company Limited are normally distributed with a mean of 3,020 grams and a standard deviation of 4 grams.

Required:
i. If a bag is picked at random, what is the probability that it weighs:

Less than 3,012 grams? (4 marks)
ii. Between 3,012 grams and 3,021.6 grams? (6 marks)
Show all the relevant normal distribution diagrams.

Answer

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Tags: Normal distribution, Pando Yam, Probability, Z-scores
Level: Level 1

Topic: Statistics
Series: MAY 2016

QTB – Nov 2015 – L1 – SA – Q11 – Statistics

This question calculates the area under the normal curve based on the given Z-score.

Question

If the z-score for a normal distribution is 1.89, then the area under the normal curve to the right of z is:

A. 0.02
B. 0.03
C. 0.04
D. 0.47
E. 0.97

Answer

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Tags: Normal distribution, Probability, Z-Score
Level: Level 1

Topic: Statistics
Series: NOV 2015

QTB – May 2015 – L1 – SB – Q2 – Statistics

Calculating probabilities related to household expenditure on mobile phones.

Question

a. more than N8,700 (5 Marks)
b. between N2,600 and N9,000 (6 Marks)
c. between N7,600 and N10,200 (6 Marks)
d. less than N8,800 (3 Marks)

Answer

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Tags: Household Expenditure, Normal distribution, Probability
Level: Level 1

Series: MAY 2015

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 – 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 – 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

QT – Nov 2018 – L1 – Q5b – Probability

Solve normal distribution problems related to spending habits of residents in Kojokrom.

Question

Required:
i) Determine the probability that a resident selected at random spends:

Less than GH¢620 (3 marks)
More than GH¢1,000 (3 marks)
Between GH¢800 and GH¢900 (4 marks)

ii) Calculate the amount:

Above which 80% of the residents will spend in a week (2 marks)
Below which 30% of the residents will spend in a week (2 marks)

Answer

Find Related Questions by Tags, levels, etc.

Tags: Continuous Variables, Normal distribution, Probability, Spending Habits, Statistics
Level: Level 1

Topic: Probability
Series: NOV 2018

Question Tag: Normal distribution

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QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

You're reporting an error for "QTB – May 2017 – L1 – SA – Q16 – Statistics"

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.

You're reporting an error for "QTB – Nov 2014 – L1 – SA – Q3 – Probability"

QTB – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q5b – Statistics"

QTB – Nov 2015 – L1 – SA – Q11 – Statistics

This question calculates the area under the normal curve based on the given Z-score.

You're reporting an error for "QTB – Nov 2015 – L1 – SA – Q11 – Statistics"

QTB – May 2015 – L1 – SB – Q2 – Statistics

Calculating probabilities related to household expenditure on mobile phones.

You're reporting an error for "QTB – May 2015 – L1 – SB – Q2 – Statistics"

QT – May 2016 – L1 – Q4 – Probability

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

You're reporting an error for "QT – May 2016 – L1 – Q4 – Probability"

QT – Nov 2017 – L1 – Q5 – Probability

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

You're reporting an error for "QT – Nov 2017 – L1 – Q5 – Probability"

QT – May 2019 – L1 – Q4b – Probability

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

You're reporting an error for "QT – May 2019 – L1 – Q4b – Probability"

QT – May 2019 – L1 – Q4a – Probability

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

You're reporting an error for "QT – May 2019 – L1 – Q4a – Probability"

QT – Nov 2018 – L1 – Q5b – Probability

Solve normal distribution problems related to spending habits of residents in Kojokrom.

You're reporting an error for "QT – Nov 2018 – L1 – Q5b – Probability"

QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

You're reporting an error for "QTB – May 2017 – L1 – SA – Q16 – Statistics"

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.

You're reporting an error for "QTB – Nov 2014 – L1 – SA – Q3 – Probability"

QTB – May 2016 – L1 – SB – Q5b – Statistics

This question involves calculating the probability of a bag of Pando Yam weighing less than a specified value using the normal distribution.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q5b – Statistics"

QTB – Nov 2015 – L1 – SA – Q11 – Statistics

This question calculates the area under the normal curve based on the given Z-score.

You're reporting an error for "QTB – Nov 2015 – L1 – SA – Q11 – Statistics"

QTB – May 2015 – L1 – SB – Q2 – Statistics

Calculating probabilities related to household expenditure on mobile phones.

You're reporting an error for "QTB – May 2015 – L1 – SB – Q2 – Statistics"

QT – May 2016 – L1 – Q4 – Probability

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

You're reporting an error for "QT – May 2016 – L1 – Q4 – Probability"

QT – Nov 2017 – L1 – Q5 – Probability

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

You're reporting an error for "QT – Nov 2017 – L1 – Q5 – Probability"

QT – May 2019 – L1 – Q4b – Probability

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

You're reporting an error for "QT – May 2019 – L1 – Q4b – Probability"

QT – May 2019 – L1 – Q4a – Probability

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

You're reporting an error for "QT – May 2019 – L1 – Q4a – Probability"

QT – Nov 2018 – L1 – Q5b – Probability

Solve normal distribution problems related to spending habits of residents in Kojokrom.

You're reporting an error for "QT – Nov 2018 – L1 – Q5b – Probability"

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