Question 1

The normal distribution has all of the following characteristics,except that

Accepted Answer

The total area under the normal distribution curve is equal to 1.0, not greater than 1.0.

Question 2

The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a

Accepted Answer

The unit of measurement along the x-axis in a standard normal distribution is referred to as a z score. This is because a standard normal distribution has a mean of 0 and a standard deviation of 1, and a z score represents the number of standard deviations from the mean that a particular score falls. Therefore, the correct answer is D, not A, B, or C.

Question 3

The ______ converts any normal distribution with any mean and any variance to a standard normal distribution with a mean of 0 and variance of 1.

Accepted Answer

The standard normal transformation, also known as standardization, converts any normal distribution with any mean and any variance to a standard normal distribution with a mean of 0 and variance of 1. This is achieved by subtracting the mean and dividing by the standard deviation of the original distribution. This transformation allows for easier comparisons and calculations for statistical analysis.

Question 4

A parent decides to reward her child if he eats an average of at least five bites of his vegetables at dinner during the first week.She finds that her child ate 4 ± 0.8 (M ± SD)bites per meal for the first week.Assuming these data are normally distributed,should this parent reward her child?

Accepted Answer

The answer of A parent decides to reward her child...

Question 5

A researcher determines that students are active about 60 ± 12 (M ± SD)min/day.Assuming these data are normally distributed,what is the z score for students being active 48 min/week?

Accepted Answer

To find the z-score, we first need to convert the 48 minutes/week to minutes/day:
48/7 = 6.86 minutes/day

Then we use the formula:

z = (x - M) / SD

where x is the value we want to convert to a z-score, M is the mean, and SD is the standard deviation.

z = (6.86 - 60) / 12
z = -4.261

Therefore, the z-score for students being active 48 min/week is -4.261, which corresponds to answer choice B (-1.0).

Question 6

The following distribution most closely approximates a

Accepted Answer

The given distribution appears to have a symmetric bell-shaped curve, which is characteristic of a normal distribution.

Question 7

The normal distribution is symmetrical,which means that

Accepted Answer

The symmetrical nature of the normal distribution means that scores above the mean are distributed the same as scores below the mean. This has practical implications in statistical analysis, as it allows for the use of a range of measures of central tendency, such as the mean, median, and mode, and makes it easier to make comparisons between different groups or populations.

Question 8

A therapist has a goal to reduce the mean number of patient symptoms expressed for a particular disorder to two symptoms per day.Following therapy,she determines that the z score for 2 symptoms per day is 0.Assuming the data are normally distributed,did she reach her goal?

Accepted Answer

A z score of 0 represents the mean. Therefore, if the therapist has reduced the mean number of symptoms expressed to 2 per day, and the z score for 2 symptoms per day is 0, then she has successfully reached her goal.

Question 9

A researcher determines that students study an average of 80 ± 20 (M ± SD)min/week.Assuming these data are normally distributed,what is the z score for students studying 60 min/week?

Accepted Answer

To calculate the z score, we need to first standardize the value using the formula:

z = (x - M) / SD

where x is the value we want to convert to a z score (in this case, x = 60), M is the mean (M = 80), and SD is the standard deviation (SD = 20). Plugging in the values, we get:

z = (60 - 80) / 20 = -1.0

Therefore, the z score for students studying 60 min/week is -1.0, which corresponds to choice B.

Question 10

A distribution of z scores is distributed in what type of unit of measurement?

Accepted Answer

A distribution of z scores is distributed in standard deviation units. Z scores represent the number of standard deviations that a data point is from the mean, and therefore are a measure of how many standard deviation units a particular value is above or below the mean of the distribution.

Question 11

The standard normal distribution is normally distributed with a mean of ______ and a variance of ______.

Accepted Answer

The standard normal distribution has a mean of 0 and a variance of 1. This is the definition of the standard normal distribution, and is not dependent on any other values for the mean or variance. Therefore, A is the correct choice as it gives the specific values for the mean and variance of the standard normal distribution.

Question 12

A theoretical distribution that evenly distributes data around the mean,median,and mode is called the

Accepted Answer

All of these terms refer to the same type of distribution, which is symmetric around the mean, median, and mode, and is characterized by its bell-shaped curve.

Question 13

What is the implication for the tails of a normal distribution being asymptotic?

Accepted Answer

The tails of a normal distribution being asymptotic means they approach but never quite reach the horizontal axis, implying that extreme scores, though increasingly rare, are possible. This characteristic highlights the potential for outliers in data that follows a normal distribution.

Question 14

In a normal distribution,50% of all data:

Accepted Answer

In a normal distribution, 50% of the data falls above the mean, and 50% falls below the mean. Since the mean, median, and mode are all equal in a perfectly symmetrical normal distribution, 50% of the data also falls below the median and above and below the mode. Therefore, all choices are correct.

Question 15

Scores far from the mean are located in the ______ of a normal distribution.

Accepted Answer

Scores far from the mean (either very high or very low) are located in the tails of a normal distribution. The majority of scores fall within one standard deviation of the mean, which is considered the body of the distribution. The most sensitive or uncertain areas of a distribution are not well-defined concepts in statistics.

Question 16

A professor finds that the students scored a 76 ± 8 (M ± SD)on the final exam.On this exam,a score of 90 is an A. Assuming these data are normally distributed, what is the z score for 90 (the cutoff for an A)?

Accepted Answer

The z score is calculated using the formula z = (X - M) / SD, where X is the score of interest (90), M is the mean score (76), and SD is the standard deviation (8). Plugging in the values: z = (90 - 76) / 8 = 14 / 8 = 1.75.

Question 17

Which of the following is a possible value for the standard deviation of a normal distribution?

Accepted Answer

The standard deviation of a normal distribution cannot be negative or infinite, which eliminates choices A and C. It can be 0, but this would result in a degenerate distribution where all values are the same. The best choice is D, where the standard deviation is a positive value that determines the spread of the distribution.

Question 18

The mean can take on any value and the standard deviation can take on any positive value.Therefore,

Accepted Answer

Since both the mean and standard deviation can vary independently to take on any value and there are infinite values that they could take, there are also an infinite number of possible normal distributions. Therefore, option C is the best choice.

Question 19

A researcher finds that the average preschool-aged child drinks two cups of milk per day.Assuming these data are normally distributed,the z score for the average cups per day in this example is

Accepted Answer

Since we do not have any information regarding the mean and standard deviation of the distribution of cups of milk consumed per day by preschool-aged children, we cannot calculate the z-score. Therefore, the z-score is exactly equal to 0.

Question 20

Most behavior is believed to ______ a normal distribution.

Accepted Answer

The normal distribution, also known as the bell curve, is a statistical pattern that describes many natural phenomena, including human behavior. Most behavior is believed to approximate a normal distribution, meaning that it falls within a range of values that cluster around the average, with fewer and fewer occurrences at the extremes. This is why normal distribution is often used in psychology and other social sciences to describe and analyze human behavior. Option A is incorrect because behavior rarely, if ever, exactly equals a normal distribution. Option B is incorrect because behavior almost always resembles a normal distribution to some degree.

Quiz 6: Probability, normal Distributions, and Z Scores