Z-scores – NBC Institute

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

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 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

Find Related Questions by Tags, levels, etc.

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

Topic: Probability
Series: MAY 2019

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

Find Related Questions by Tags, levels, etc.

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

Topic: Statistics
Series: MAY 2016

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

Find Related Questions by Tags, levels, etc.

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

Topic: Probability
Series: MAY 2016

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

Find Related Questions by Tags, levels, etc.

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

Topic: Probability
Series: MAY 2019

Question Tag: Z-scores

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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.

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 2019 – L1 – Q4b – Probability

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

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.

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 2019 – L1 – Q4b – Probability

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

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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.

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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 – 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"

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"

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 – 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"

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