### Probability And Normal Distribution, Distribution, Statistics Final Test

The key terms in these Statistics chapters include Normal Distribution, Sampling With Replacement, Distribution, Sample, Probability, Random Sample, Proportions, z-score, Probability And Normal Distribution, Frequency Distribution Graph, Bar Graph. Final Test is based on these chapters.

A class consists of 10 males and 30 females. A random sample of n = 3 students is selected. If their first two students are both females, what is the probability that the third student is a male?

a) 10/37

b) 10/38**c) 10/40**

d) 9/38

All probabilities can be expressed as decimal values ranging from 0 to 1.00.

**True**

Which of the following is a requirement for a random sample?

a) every individual has an equal chance of being selected

b) the probabilities cannot change during a series of selections

c) there must be sampling with replacement**d) all of the other 3 choices are correct**

A class consists of 10 males and 30 females. If one student is randomly selected from the class, what is the probability of selecting a male?

a) 10/30**b) 10/40**

c) 1/10

d) 1/40

Which of the following accurately describes the proportions in the tails of a normal distribution?

a) proportions in the right-hand tail are positive, and proportions in the left-hand tail are negative

b) proportions in the right-hand tail are negative, and proportions in the left-hand tail are positive**c) proportions in both tails are positive**

d) proportions in both tails are negative

Which of the following accurately describes the proportions in the body of a normal distribution?

a) body proportions on the right side of the z-score are greater than 0.50; on the left side, they are less than 0.50

b) body proportions on the right side of the z-score are less than 0.50; on the left side, they are greater than 0.50

c) body proportions on either side of the z-score are less than 0.50**d) body proportions on either side of the z-score are greater than 0.50**

The probability of randomly selecting a red marble from a jar that contains 10 red marbles and 20 blue marbles is 1/30.

**False**

If a distribution of scores is shown in a bar graph, you know that the scores were measured on a(n) _________ scale of measurement.

**Nominal or ordinal**

In a frequency distribution graph, frequencies are presented on the ______, and the scores (categories) are listed on the_____.

**Y axis; X axis**

Which of the following accurately describes the proportions in the tails of a normal distribution?

a) proportions in the right-hand tail are greater than 0.50, and proportions in the left-hand tail are less than 0.50

b) proportions in the right-hand tail are less than 0.50, and proportions in the left-hand tail are greater than 0.50**c) proportions in both tails are less than 0.50**

d) proportions in both tails are greater than 0.50

What proportion of a normal distribution is located in the tail beyond z = 1.50?

a) 0.9332**b) 0.0668**

c) 0.4332

d) 0.1336

What proportion of a normal distribution is located between the mean and z = 1.40?

a) 0.9192

b) 0.0808**c) 0.4192**

d) 0.8384

A vertical line drawn through a normal distribution at z = 0.50 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body?

**a) 0.6915**

b) 0.3085

c) 0.1915

d) 0.3830

A vertical line is drawn through a normal distribution so that 47.5% of the distribution is located between the line and the mean. The line is drawn at z = 1.96 or at z -1.96.

**True**

For a normal distribution, the z-score boundary that separates the highest 2.5% of the scores from the rest is z = -1.96.

**False**

What proportion of a normal distribution is located between z = -1.50 and z = +1.50?

a) 0.9332

b) 0.0668

c) 0.4332**d) 0.8664**

What is the probability of randomly selecting a z-score less than z = 1.25 from a normal distribution?

**a) 0.8944**

b) 0.1056

c) 0.3944

d) 0.2112

What z-score value separates the highest 10% of the scores in a normal distribution from the lowest 90%?

**a) z = 1.28**

b) z = 0.25

c) z = -1.28

d) z = -0.25

For a normal distribution, proportions in the right-hand tail are positive, and proportions in the left-hand tail are negative.

**False**

The proportion in the tail of a normal distribution can never be more than 0.50.

**True**

A sample of n = 15 scores ranges from a high of X = 11 to a low of X = 3. If these scores are placed in a frequency distribution table, how many X values will be listed in the first column?

**9**

A professor records the number of students who are absent each day for the semester. Because this is a discrete variable, a bar graph should be used to show the frequency distribution.

**FALSE**

The tail is on the right side of a normal distribution for any z-score value greater than zero.

**True**

A vertical line drawn through a normal distribution at z = -0.50 separates the distribution into two sections. The proportions in the larger section is 0.6915.

**True**

For any normal distribution, the proportion in the tail beyond z = 2.00 is p = 0.0228.

**True**

Scores on the SAT form a normal distribution with a mean of u = 500 with ao = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?

**a) X = 475**

b) X = 525

c) X = 440

d) X = 560

John drives to work each morning, and the trip takes an average of u = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of ao = 5 minutes. For a randomly selected morning, what is the probability that John’s drive to work will take less than 35 minutes?

a) 0.6554

b) 0.3446

c) 0.7257**d) 0.2743**

IQ scores form a normal distribution with u = 100 and ao = 15. Individuals with IQs between 90 and 110 are classified as average. What proportion of the population is average?

a) 0.7486

b) 0.5028**c) 0.4972**

d) 0.2486

IQ scores form a normal distribution with u = 100 and ao = 15. Individuals with IQs above 140 are classified in the genius category. What proportion of the population consists of geniuses?

a) 0.9962

b) 0.5038

c) 0.4962**d) 0.0038**

A class consists of 10 males and 30 females. A random sample of n = 3 students is selected. If their first two students are both females, what is the probability that the third student is a male?

a) 10/37

b) 10/38**c) 10/40**

d) 9/38

All probabilities can be expressed as decimal values ranging from 0 to 1.00.

**True**

Which of the following is a requirement for a random sample?

a) every individual has an equal chance of being selected

b) the probabilities cannot change during a series of selections

c) there must be sampling with replacement**d) all of the other 3 choices are correct**

A class consists of 10 males and 30 females. If one student is randomly selected from the class, what is the probability of selecting a male?

a) 10/30**b) 10/40**

c) 1/10

d) 1/40

Which of the following accurately describes the proportions in the tails of a normal distribution?

a) proportions in the right-hand tail are positive, and proportions in the left-hand tail are negative

b) proportions in the right-hand tail are negative, and proportions in the left-hand tail are positive**c) proportions in both tails are positive**

d) proportions in both tails are negative

Which of the following accurately describes the proportions in the body of a normal distribution?

a) body proportions on the right side of the z-score are greater than 0.50; on the left side, they are less than 0.50

b) body proportions on the right side of the z-score are less than 0.50; on the left side, they are greater than 0.50

c) body proportions on either side of the z-score are less than 0.50**d) body proportions on either side of the z-score are greater than 0.50**

The probability of randomly selecting a red marble from a jar that contains 10 red marbles and 20 blue marbles is 1/30.

**False**

If a distribution of scores is shown in a bar graph, you know that the scores were measured on a(n) _________ scale of measurement.

**Nominal or ordinal**

In a frequency distribution graph, frequencies are presented on the ______, and the scores (categories) are listed on the_____.

**Y axis; X axis**

Which of the following accurately describes the proportions in the tails of a normal distribution?

a) proportions in the right-hand tail are greater than 0.50, and proportions in the left-hand tail are less than 0.50

b) proportions in the right-hand tail are less than 0.50, and proportions in the left-hand tail are greater than 0.50**c) proportions in both tails are less than 0.50**

d) proportions in both tails are greater than 0.50

What proportion of a normal distribution is located in the tail beyond z = 1.50?

a) 0.9332**b) 0.0668**

c) 0.4332

d) 0.1336

What proportion of a normal distribution is located between the mean and z = 1.40?

a) 0.9192

b) 0.0808**c) 0.4192**

d) 0.8384

A vertical line drawn through a normal distribution at z = 0.50 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body?

**a) 0.6915**

b) 0.3085

c) 0.1915

d) 0.3830

A vertical line is drawn through a normal distribution so that 47.5% of the distribution is located between the line and the mean. The line is drawn at z = 1.96 or at z -1.96.

**True**

For a normal distribution, the z-score boundary that separates the highest 2.5% of the scores from the rest is z = -1.96.

**False**

What proportion of a normal distribution is located between z = -1.50 and z = +1.50?

a) 0.9332

b) 0.0668

c) 0.4332**d) 0.8664**

What is the probability of randomly selecting a z-score less than z = 1.25 from a normal distribution?

**a) 0.8944**

b) 0.1056

c) 0.3944

d) 0.2112

What z-score value separates the highest 10% of the scores in a normal distribution from the lowest 90%?

**a) z = 1.28**

b) z = 0.25

c) z = -1.28

d) z = -0.25

For a normal distribution, proportions in the right-hand tail are positive, and proportions in the left-hand tail are negative.

**False**

The proportion in the tail of a normal distribution can never be more than 0.50.

**True**

A sample of n = 15 scores ranges from a high of X = 11 to a low of X = 3. If these scores are placed in a frequency distribution table, how many X values will be listed in the first column?

**9**

A professor records the number of students who are absent each day for the semester. Because this is a discrete variable, a bar graph should be used to show the frequency distribution.

**F**alse

The tail is on the right side of a normal distribution for any z-score value greater than zero.

**True**

A vertical line drawn through a normal distribution at z = -0.50 separates the distribution into two sections. The proportions in the larger section is 0.6915.

**True**

For any normal distribution, the proportion in the tail beyond z = 2.00 is p = 0.0228.

**True**

Scores on the SAT form a normal distribution with a mean of u = 500 with ao = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?

**a) X = 475**

b) X = 525

c) X = 440

d) X = 560

John drives to work each morning, and the trip takes an average of u = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of ao = 5 minutes. For a randomly selected morning, what is the probability that John’s drive to work will take less than 35 minutes?

a) 0.6554

b) 0.3446

c) 0.7257**d) 0.2743**

IQ scores form a normal distribution with u = 100 and ao = 15. Individuals with IQs between 90 and 110 are classified as average. What proportion of the population is average?

a) 0.7486

b) 0.5028**c) 0.4972**

d) 0.2486