Question 1

Assuming a confidence interval of 95% (z = 1.96), calculate the width of the confidence interval for n = 65, = 24.5, s = 4.5 (1 decimal place)

Accepted Answer

A)  24.5 ± 0.8 
B)  24.5 ± 0.9 
C)  24.5 ± 1.0 
D)  24.5 ± 1.1 
A)  24.5 ± 0.8 
B)  24.5 ± 0.9 
C)  24.5 ± 1.0 
D)  24.5 ± 1.1 D

Question 2

If the normal distribution is to be used as an approximation to the binomial with n = 200 and p = 0.78 what value should be used to approximate the standard deviation (1 decimal place)?

Accepted Answer

A)  5.8 
B)  5.9 
C)  6.0 
D)  6.1 
A)  5.8 
B)  5.9 
C)  6.0 
D)  6.1 B

Question 3

What name is given to a value that has been standardized?

Accepted Answer

A)  Mean 
B)  Z-score 
C)  Standard Deviation 
D)  Variance 
A)  Mean 
B)  Z-score 
C)  Standard Deviation 
D)  Variance B

Question 4

Last year average wages in an Indian firm were INR 109,658, a sample of 30 employees in the same firm this year gives an average wage of INR 110,986 (standard deviation INR 1,234). Is this evidence of a significant difference in wages?

Accepted Answer

A)  No, -1.96  1.96 
D)  There is no evidence of a significant difference 
A)  No, -1.96  1.96 
D)  There is no evidence of a significant difference

Question 5

Which of the following statements about the normal distribution are NOT true?

Accepted Answer

A)  The normal distribution is symmetrically shaped 
B)  The normal distribution is centred around the mean 
C)  The normal distribution shows a clustering of values around the mean 
D)  The normal distribution is not suitable for use with continuous data 
A)  The normal distribution is symmetrically shaped 
B)  The normal distribution is centred around the mean 
C)  The normal distribution shows a clustering of values around the mean 
D)  The normal distribution is not suitable for use with continuous data

Question 6

Calculate the Z-score for a value of 34 when mean = 24 and standard deviation = 4

Accepted Answer

A)  2.0 
B)  2.2 
C)  2.5 
D)  2.8 
A)  2.0 
B)  2.2 
C)  2.5 
D)  2.8

Question 7

A sample of components made by a factory in China shows that 6 out of a sample of 50 were found to be faulty. What is the width of a 95% confidence interval (z = 1.96) for the defect rate (2 decimal places)?

Accepted Answer

A)  0.12 ± 0.06 
B)  0.12 ± 0.09 
C)  0.12 ± 0.12 
D)  0.12 ± 0.15 
A)  0.12 ± 0.06 
B)  0.12 ± 0.09 
C)  0.12 ± 0.12 
D)  0.12 ± 0.15

Question 8

If the probability that a Z-score lies between 0 and 2 is 0.452 then what is the probability that Z < 2?

Accepted Answer

A)  0.4772 
B)  0.5 
C)  0.9772 
D)  0.0228 
A)  0.4772 
B)  0.5 
C)  0.9772 
D)  0.0228

Question 9

The diameter of holes drilled into flat-pack furniture is normally distributed with a mean of 5mm and a standard deviation of 0.15mm. If a single item of furniture has 50 holes in it, how many have a diameter of more than 5.2mm (to the nearest whole number)?

Accepted Answer

A)  5 
B)  6 
C)  7 
D)  8 
A)  5 
B)  6 
C)  7 
D)  8

Question 10

Analysis of a sample of 50 of the second quarter sales of a Dubai fashion store shows a difference ( - ) of AED 236, z = +2.37 indicating that the difference is significant. Calculate the standard deviation of the sample (1 decimal place).

Accepted Answer

A)  AED 697.3 
B)  AED 704.1 
C)  AED 723.6 
D)  AED 734.9 
A)  AED 697.3 
B)  AED 704.1 
C)  AED 723.6 
D)  AED 734.9

Exam 34: Normal Distribution

Assuming a confidence interval of 95% (z = 1.96), calculate the width of the confidence interval for n = 65, = 24.5, s = 4.5 (1 decimal place)

If the normal distribution is to be used as an approximation to the binomial with n = 200 and p = 0.78 what value should be used to approximate the standard deviation (1 decimal place)?

What name is given to a value that has been standardized?

Last year average wages in an Indian firm were INR 109,658, a sample of 30 employees in the same firm this year gives an average wage of INR 110,986 (standard deviation INR 1,234). Is this evidence of a significant difference in wages?

Which of the following statements about the normal distribution are NOT true?

Calculate the Z-score for a value of 34 when mean = 24 and standard deviation = 4

A sample of components made by a factory in China shows that 6 out of a sample of 50 were found to be faulty. What is the width of a 95% confidence interval (z = 1.96) for the defect rate (2 decimal places)?

If the probability that a Z-score lies between 0 and 2 is 0.452 then what is the probability that Z < 2?

The diameter of holes drilled into flat-pack furniture is normally distributed with a mean of 5mm and a standard deviation of 0.15mm. If a single item of furniture has 50 holes in it, how many have a diameter of more than 5.2mm (to the nearest whole number)?

Analysis of a sample of 50 of the second quarter sales of a Dubai fashion store shows a difference ( - ) of AED 236, z = +2.37 indicating that the difference is significant. Calculate the standard deviation of the sample (1 decimal place).

Introduction to Business Mathematics and Statistics

Sampling and Data Collection

Data and Their Accuracy

Frequency Distributions and Charts

General Charts and Graphs

Arithmetic Mean

Median

Mode and Other Measures of Location

Measures of Dispersion and Skewness

Standard Deviation

Quantiles and the Quartile Deviation

Linear Functions and Graphs

Regression Techniques

Correlation Techniques

Time Series Model

Time Series Trend

Seasonal Variation and Forecasting

Index Relatives

Composite Index Numbers

Special Published Indices

Interest and Depreciation

Present Value and Investment Appraisal

Annuities

Functions and Graphs

Linear Equations

Quadratic and Cubic Equations

Differentiation and Integration

Cost, Revenue and Profit Functions

Set Theory and Enumeration

Introduction to Probability

Conditional Probability and Expectation

Combinations and Permutations

Binomial and Poisson Distributions

Linear Inequalities

Matrices

Inventory Control

Network Planning and Analysis

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