Question 1

Which two characteristics describe normal curve distribution?
A) theoretical and unimodal (single peak)
B) symmetrical and bimodal (two peaks)
C) symmetrical and short-tailed
D) symmetrical and commonly occurring for most observable variables in the real world

Accepted Answer

A

Question 2

Consider two normal distributions. Normal Distribution A has  = 50 and s = 4. Normal Distribution B has  = 15 and s = 2. How does the total area under the curve differ between Distribution A and Distribution B when we move from the mean to +1 standard deviation along the curve's horizontal axis (abscissa)?
A) The area is half as large for Distribution A compared to Distribution B.
B) The area under the curve is equal for Distribution A and Distribution B.
C) The area is twice as big for Distribution A compared to Distribution B.
D) The area is four times as big for Distribution A compared to Distribution B.

Accepted Answer

B

Question 3

Where do the tails of the theoretical normal curve touch the horizontal axis?
A) just past the 3rd standard deviation
B) between the 3rd and 4th standard deviations
C) at approximately the 5th standard deviation
D) They never touch the horizontal axis.

Accepted Answer

The tails of the theoretical normal curve extend infinitely in both directions and never actually touch the horizontal axis.

Question 4

What percentage of the total area is between the mean and +1 standard deviation for a normal curve?
A) about 34%
B) about 68%
C) about 80%
D) about 99.7%

Accepted Answer

In a normal distribution, approximately 34% of the data falls between the mean and +1 standard deviation.

Question 5

For a sample of 100 nursing home residents where we assume blood pressure to be normally distributed, approximately how many people would be two standard deviations below the mean blood pressure?
A) approximately 1 resident
B) approximately 2 residents
C) approximately 10 residents
D) approximately 32 residents

Accepted Answer

The answer of For a sample of 100 nursing home...

Question 6

A Z score of -0.5 means that the case's raw score is how much less than the sample mean?
A) five standard deviations less than the mean
B) half a raw unit deviation less than the mean
C) half a standard deviation less than the mean
D) It is impossible to answer without knowing the size of the sample's standard deviation.

Accepted Answer

A Z score of -0.5 indicates that the raw score is half a standard deviation below the mean.

Question 7

For a curve that is NOT normally distributed, what percentage of the area will be beyond ±1.5 standard deviations?
A) about 97%
B) about 68%
C) about 13.4%
D) It's impossible to say.

Accepted Answer

For a non-normally distributed curve, the percentage of area beyond ±1.5 standard deviations cannot be determined without additional information about the distribution.

Question 8

Suppose 50 hockey players tried out for a team, and their skating speed for a 100-metre dash was normally distributed. What would be the mean and standard deviation for the normal distribution characterizing their skate times?
A) a mean of 0 and a standard deviation of 0
B) a mean of 0 and a standard deviation of 1
C) a mean of 10 and a standard deviation of 20
D) a mean of 50 and a standard deviation of 1

Accepted Answer

In a standard normal distribution, the mean is 0 and the standard deviation is 1.

Question 9

A researcher obtains robbery rates for 23 cities for 2016. She standardizes the robbery rate variable. What happens to the variable's scores?
A) Each will be identical to the median city's score.
B) Each will be identical to the standard deviation.
C) Each will be turned into a Z score.
D) The mean will be equal to 1.

Accepted Answer

Standardizing a variable involves converting its scores into Z scores, which represent the number of standard deviations each score is from the mean.

Question 10

What is the value of the corresponding raw score if a Z score is 0?
A) zero
B) a negative number
C) the same as the standard deviation of the empirical distribution
D) the same as the mean of the empirical distribution

Accepted Answer

A Z score of 0 indicates that the raw score is exactly at the mean of the distribution.

Question 11

What is the process for finding the area above a positive Z score or below a negative Z score?
A) Use the "Area Beyond Z" column C of the Z-score table.
B) Add the area between the Z score and the mean to 100%.
C) Subtract the value of the Z score from the mean.
D) Add the value of the Z score to the area beyond the mean.

Accepted Answer

The "Area Beyond Z" column in the Z-score table provides the area in the tail of the distribution, which is the area above a positive Z score or below a negative Z score.

Question 12

What property of the normal curve ensures that the area from the mean to -2 standard deviations is the same as the area from the mean to +2 standard deviations?
A) the least squares principle of the normal distribution
B) the skewness of the normal distribution
C) the symmetry of the normal distribution
D) the interval-ratio measurement of the normal distribution

Accepted Answer

The normal distribution is symmetric about the mean, meaning the area on either side of the mean is equal for equidistant points.

Question 13

The mean score on a physiology test was 71, and the standard deviation of scores was 9. Assuming a normal distribution, what percentage of scores fell below a 60?
A) 11.12%
B) 19.44%
C) 25%
D) 45.71%

Accepted Answer

To find the percentage of scores below 60, we calculate the z-score: z = (60 - 71) / 9 = -1.22. Using a standard normal distribution table, a z-score of -1.22 corresponds to approximately 11.12% of scores falling below 60.

Question 14

What is the process for obtaining the area between the scores when the Z scores of two tests' scores are +1.2 and +1.5?
A) Find the area between each score and the mean in the Z-score table, and then subtract the smaller area from the larger area.
B) Find the area beyond each score in the Z-score table, and subtract the difference between the areas from the mean.
C) Subtract the Z scores and find the area of the difference in the Z-score table.
D) Find the area between each score and the mean in the Z-score table, and then subtract the difference between them from 100%.

Accepted Answer

To find the area between two Z scores, you look up each Z score in the Z-score table to find the area between each score and the mean, then subtract the smaller area from the larger area to get the area between the two scores.

Question 15

A set of 80 sociology tests with a normal distribution has a mean score of 65 and a standard deviation of 8. Shellie scored in the 90th percentile of the class. What score did she receive? A) 0.52 = (X_i + 65)/8 = 60.84 B) 1.28 = (65 - X_i)/80 = 63.44 C) 1.28 = (X_i - 65)/8 = 75.24 D) 100 = (X_i + 10)/1 = 90

Accepted Answer

The 90th percentile corresponds to a z-score of approximately 1.28. Using the formula X = μ + zσ, where μ is the mean and σ is the standard deviation, Shellie's score is 65 + 1.28(8) = 75.24.

Question 16

What is the process for determining the area between two negative Z scores?
A) Find the area between each Z score and the mean, and subtract the smaller area from the larger.
B) Add the Z scores and find the area below the total Z score.
C) Subtract the two negative Z scores and find the total area above the total Z score.
D) Find the area between each Z score and the mean, and add the areas.

Accepted Answer

To find the area between two negative Z scores, calculate the area from the mean to each Z score and subtract the smaller area from the larger area.

Question 17

In what sense is the normal distribution a distribution of probabilities?
A) The normal distribution tells us that cases are equally likely to have any value within ±3 standard deviations from the mean.
B) The normal distribution allows us to estimate the precise likelihood of selecting a case that has a score within a certain range.
C) The normal distribution indicates that scores above the mean are more probable than scores with negative Z values.
D) The normal distribution tells us that half of all cases will probably fall within ±1 standard deviation from the mean.

Accepted Answer

The normal distribution is a probability distribution that allows us to estimate the likelihood of a random variable falling within a particular range of values, based on its mean and standard deviation.

Question 18

A social work researcher constructed a measure of quality of life and obtained a distribution of scores on this measure from a randomly selected sample of elderly persons. The scores were normally distributed, with a mean of 45 and a standard deviation of 7. What is the probability that a randomly selected case from the sample will have a score less than 38?
A) 0.5200
B) 0.5018
C) 0.4526
D) 0.1587

Accepted Answer

The Z-score for a score of 38 is (38-45)/7 = -1. The probability of a Z-score being less than -1 in a standard normal distribution is approximately 0.1587.

Question 19

What is the probability of rolling a 1 in a single toss of a six-sided die?
A) 1 in 60
B) 1 in 6
C) 1 in 5
D) 5 in 6

Accepted Answer

There are six possible outcomes when rolling a six-sided die, and only one of them is a 1. Therefore, the probability of rolling a 1 is 1 in 6.

Question 20

If it rains 21 of 30 days in a month, what value represents the probability of rain occurring on a single day chosen at random from the month?
A) 21/30 = 0.70
B) (30 - 21)/9 = 1
C) 30/21 = 1.43
D) (21 + 30)/21 = 2.43

Accepted Answer

The probability of rain on a single day is the number of rainy days divided by the total number of days, which is 21/30 = 0.70.

Quiz 4: The Normal Curve

Which two characteristics describe normal curve distribution?

Where do the tails of the theoretical normal curve touch the horizontal axis?

What percentage of the total area is between the mean and +1 standard deviation for a normal curve?

For a sample of 100 nursing home residents where we assume blood pressure to be normally distributed, approximately how many people would be two standard deviations below the mean blood pressure?

A Z score of -0.5 means that the case's raw score is how much less than the sample mean?

For a curve that is NOT normally distributed, what percentage of the area will be beyond ±1.5 standard deviations?

Suppose 50 hockey players tried out for a team, and their skating speed for a 100-metre dash was normally distributed. What would be the mean and standard deviation for the normal distribution characterizing their skate times?

A researcher obtains robbery rates for 23 cities for 2016. She standardizes the robbery rate variable. What happens to the variable's scores?

What is the value of the corresponding raw score if a Z score is 0?

What is the process for finding the area above a positive Z score or below a negative Z score?

What property of the normal curve ensures that the area from the mean to -2 standard deviations is the same as the area from the mean to +2 standard deviations?

The mean score on a physiology test was 71, and the standard deviation of scores was 9. Assuming a normal distribution, what percentage of scores fell below a 60?

What is the process for obtaining the area between the scores when the Z scores of two tests' scores are +1.2 and +1.5?

A set of 80 sociology tests with a normal distribution has a mean score of 65 and a standard deviation of 8. Shellie scored in the 90th percentile of the class. What score did she receive?

What is the process for determining the area between two negative Z scores?

In what sense is the normal distribution a distribution of probabilities?

What is the probability of rolling a 1 in a single toss of a six-sided die?

If it rains 21 of 30 days in a month, what value represents the probability of rain occurring on a single day chosen at random from the month?