Question 1

Any set of normally distributed data can be transformed to its standardised form.

Accepted Answer

Standardizing data involves transforming it to have a mean of 0 and a standard deviation of 1. This can be done for any normally distributed data set.

Question 2

The value of the cumulative standardised normal distribution at 1.5X is 0.9332.The value of X is

Accepted Answer

The cumulative standardised normal distribution value of 0.9332 corresponds to a Z-score of approximately 1.5. Since the value is given at 1.5X, and we know the Z-score is 1.5, it implies X = 1.00 to satisfy the condition 1.5X = 1.5.

Question 3

In its standardised form,the normal distribution

Accepted Answer

The standardised form of the normal distribution has a mean of 0 and a standard deviation of 1. This means that any normal distribution can be transformed into the standard normal distribution by subtracting the mean and dividing by the standard deviation. The standard normal distribution has many useful properties and is widely used in statistics and probability theory. Choices A, B, and D are incorrect because they do not correctly describe the standardised form of the normal distribution.

Question 4

The probability that a standard normal random variable,Z,falls between -2.00 and -0.44 is 0.6472.

Accepted Answer

The answer of The probability that a standard normal random...

Question 5

The probability that a standard normal random variable,Z,is less than 50 is approximately 0.

Accepted Answer

The answer of The probability that a standard normal random...

Question 6

The value of the cumulative standardised normal distribution at Z is 0.6255.The value of Z is

Accepted Answer

The answer of The value of the cumulative standardised normal...

Question 7

The probability that a standard normal random variable,Z,is between 1.00 and 3.00 is 0.1574.

Accepted Answer

This statement is true. When we look at a standard normal distribution table, we can see that the area between 1.00 and 3.00 is 0.1574 or 15.74%. Therefore, the probability of a standard normal random variable being between 1.00 and 3.00 is indeed 0.1574.

Question 8

The "middle spread",that is the middle 50% of the normal distribution,is equal to one standard deviation.

Accepted Answer

The middle 50% of the normal distribution, also known as the interquartile range, actually spans approximately 1.35 standard deviations, not one standard deviation.

Question 9

If a particular batch of data is approximately normally distributed,we would find that approximately

Accepted Answer

The statements in options A, B, and C are all approximations based on the properties of the normal distribution. Specifically, about 95% of observations fall within ±2 standard deviations (A), about 80% within ±1.28 standard deviations (B), and about 68% within ±1 standard deviation (C) from the mean in a normal distribution.

Question 10

A worker earns $15 per hour at a plant and is told that only 2.5% of all workers make a higher wage.If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour,the average wage for the plant is $7.50 per hour.

Accepted Answer

The statement contradicts itself. If only 2.5% of all workers make a higher wage, the average wage cannot be $7.50 per hour. Additionally, more information is needed to assume that the wage is normally distributed.

Question 11

Which of the following can be used to model the distribution of the values for a continuous random variable?

Accepted Answer

All of the options listed, Exponential distribution, Uniform distribution, and Normal distribution, are models used to describe the distribution of values for continuous random variables. Each serves different types of data and scenarios.

Question 12

The probability that a standard normal random variable,Z,is below 1.96 is 0.4750.

Accepted Answer

The answer of The probability that a standard normal random...

Question 13

For some positive value of Z,the value of the cumulative standardised normal distribution is 0.8340.The value of Z is

Accepted Answer

The answer of For some positive value of Z,the value...

Question 14

Theoretically,the mean,median,and the mode are all equal for a normal distribution.

Accepted Answer

This is a property of a normal distribution, which is a symmetric distribution with the highest frequency at its mean.

Question 15

The probability that a standard normal random variable,Z,falls between -1.50 and 0.81 is 0.7242.

Accepted Answer

This statement is true according to the standard normal distribution table or a calculator with a normal distribution function.

Question 16

Which of the following about the normal distribution is NOT true?

Accepted Answer

The normal distribution is a continuous probability distribution, not a discrete one.

Question 17

The normal distribution is related to the Central Limit Theorem.

Accepted Answer

The Central Limit Theorem states that the distribution of sample means becomes approximately normal as the sample size increases, and the normal distribution is often used to approximate the distribution of sample means.

Question 18

The probability that a standard normal random variable,Z,is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.

Accepted Answer

This is true because the standard normal distribution is symmetric about zero. Therefore, the probability of Z being between 1.50 and 2.10 is the same as the probability of Z being between -2.10 and -1.50.

Question 19

The value of the cumulative standardised normal distribution at Z is 0.8770.The value of Z is

Accepted Answer

Using a standard normal distribution table, we can find that the Z-score associated with a cumulative standardised normal distribution of 0.8770 is 1.16.

Question 20

For some value of Z,the probability that a standard normal variable is below Z is 0.2090.The value of Z is

Accepted Answer

The value of Z that corresponds to a probability of 0.2090 in a standard normal distribution is approximately -0.81. This is found by looking up the probability in a Z-table or using a statistical tool to find the Z-score that corresponds to the lower tail probability of 0.2090.

Quiz 6: The Normal Distribution and Other Continuous Distributions

Any set of normally distributed data can be transformed to its standardised form.

The value of the cumulative standardised normal distribution at 1.5X is 0.9332.The value of X is

In its standardised form,the normal distribution

The probability that a standard normal random variable,Z,falls between -2.00 and -0.44 is 0.6472.

The probability that a standard normal random variable,Z,is less than 50 is approximately 0.

The value of the cumulative standardised normal distribution at Z is 0.6255.The value of Z is

The probability that a standard normal random variable,Z,is between 1.00 and 3.00 is 0.1574.

The "middle spread",that is the middle 50% of the normal distribution,is equal to one standard deviation.

If a particular batch of data is approximately normally distributed,we would find that approximately

A worker earns $15 per hour at a plant and is told that only 2.5% of all workers make a higher wage.If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour,the average wage for the plant is $7.50 per hour.

Which of the following can be used to model the distribution of the values for a continuous random variable?

The probability that a standard normal random variable,Z,is below 1.96 is 0.4750.

For some positive value of Z,the value of the cumulative standardised normal distribution is 0.8340.The value of Z is

Theoretically,the mean,median,and the mode are all equal for a normal distribution.

The probability that a standard normal random variable,Z,falls between -1.50 and 0.81 is 0.7242.

Which of the following about the normal distribution is NOT true?

The normal distribution is related to the Central Limit Theorem.

The probability that a standard normal random variable,Z,is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.

The value of the cumulative standardised normal distribution at Z is 0.8770.The value of Z is

For some value of Z,the probability that a standard normal variable is below Z is 0.2090.The value of Z is