Question 1

Roughly __________ of the total area under the normal curve rests between two standard Deviations above and below the mean.

Accepted Answer

Approximately 95% of the total area under the normal curve lies within two standard deviations above and below the mean.

Question 2

A probability distribution is essentially a frequency distribution of percentages for:

Accepted Answer

A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range. This concept applies to an infinite number of cases, not just a finite or small number of cases, because it encompasses all potential outcomes and their probabilities.

Question 3

In a symmetrical distribution, what percent of the scores fall above the mean?

Accepted Answer

In a symmetrical distribution, 50% of the scores fall above the mean and 50% fall below the mean.

Question 4

If the probability (p) of giving birth to a boy is .51, and a woman can only give birth to a Single boy or girl, then the probability of giving birth to a girl is:

Accepted Answer

The probability of giving birth to a girl is 1 minus the probability of giving birth to a boy (1 - p), and since p = .51, the probability of giving birth to a girl is 1 - .51 = .49.

Question 5

The probability of a student correctly guessing the answer to this question is:

Accepted Answer

The question has four options, so the probability of correctly guessing one is 1 out of 4, or 25%.

Question 6

The probability of flipping 2 heads in 2 flips of the same coin is:

Accepted Answer

The probability of flipping a head on one flip is 1/2. Since the flips are independent, the probability of flipping two heads in two flips is (1/2) * (1/2) = 1/4 or 25%.

Question 7

Which of the following is true of the normal distribution?

Accepted Answer

The normal distribution is characterized by its symmetrical, bell-shaped curve that is unimodal (having one peak), and its tails that extend indefinitely in both directions, approaching but never touching the horizontal axis. This means all the given statements A, B, and C are true characteristics of the normal distribution.

Question 8

Roughly __________ of the total area under the normal curve rests between the mean and One standard deviation above the mean.

Accepted Answer

Approximately 34% of the total area under the normal curve lies between the mean and one standard deviation above the mean.

Question 9

The question below refers to the following situation:
The average price for a new car is $18,000 and the standard deviation is $1,500. Calculate The z scores for the following individual score:
If X = 19,000, z = __________.

Accepted Answer

The z-score is calculated using the formula z = (X - μ) / σ, where X is the individual score, μ is the mean, and σ is the standard deviation. Substituting the given values: z = (19,000 - 18,000) / 1,500 = 1,000 / 1,500 = 0.67.

Question 10

A normal curve:

Accepted Answer

The normal curve, also known as the Gaussian distribution, is a theoretical model used to describe the distribution of many types of data. It is fundamental in statistics for describing distributions and making decisions based on statistical analysis.

Question 11

Empirical probability distributions are those dependent on:

Accepted Answer

Empirical probability distributions are based on observations or experiments from which data is collected. This data is then used to determine or estimate the values of the probability distribution, making observation the key factor.

Question 12

If 68% of IQ scores are between 85 and 115, what is the probability of meeting a person in The population within that IQ range?

Accepted Answer

The probability is directly given as 68%, which in decimal form is 0.68.

Question 13

The question below refers to the following situation:
The average price for a new car is $18,000 and the standard deviation is $1,500. Calculate The z scores for the following individual score:
If X = 21,000, z = __________.

Accepted Answer

The z-score is calculated using the formula z = (X - μ) / σ, where X is the individual score, μ is the mean, and σ is the standard deviation. Plugging in the given values: z = (21000 - 18000) / 1500 = 3000 / 1500 = 2.00.

Question 14

A probability distribution has:

Accepted Answer

A probability distribution typically has both a mean and a standard deviation, which are measures of central tendency and dispersion, respectively.

Question 15

The probability of rolling a '4' on one toss of a standard six-sided die is:

Accepted Answer

The probability of rolling a '4' on a six-sided die is 1 out of 6 possible outcomes, which can be represented as the fraction 1/6. When converted to a decimal, it is approximately 0.167.

Question 16

The normal curve is:

Accepted Answer

The normal curve is a theoretical ideal used in statistics to represent the distribution of many types of data. Real-life data might not always follow a perfect normal distribution, and the normal curve is not positively skewed; it is symmetric.

Question 17

Which of the following is NOT true of the normal curve?

Accepted Answer

The normal curve is symmetric, not skewed, meaning its tails extend equally in both directions from the center. This symmetry results in the mode, median, and mean being identical, making it a probability distribution where the total area under the curve represents 100% of cases.

Question 18

The question below refers to the following situation:
The average price for a new car is $18,000 and the standard deviation is $1,500. Calculate The z scores for the following individual score:
If X = 16,000, z = __________.

Accepted Answer

The z-score is calculated using the formula z = (X - μ) / σ, where X is the individual score, μ is the mean, and σ is the standard deviation. Plugging in the given values: z = (16,000 - 18,000) / 1,500 = -2,000 / 1,500 = -1.33.

Question 19

Probability is defined as:

Accepted Answer

The answer of Probability is defined as: 
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Question 20

Which of the following is true of probabilities?

Accepted Answer

A probability of an event varies from 0 to 1.0, where 0 means the event is impossible and 1.0 means the event is certain to occur.

Quiz 5: Probability and the Normal Curve