### Normal Distribution, Probability, Z-Score, Distribution – Statistic Quiz

The key terms in these Statistic chapters include Normal Distribution, Distribution, Probability, Proportion, z-score, Sample, Hypothesis, Population, Mean, IQ Scores, Random Sample, Hypothesis Test, Null Hypothesis, Population Mean, Left-hand Tail, Right-hand Tail, Random Sample.

A normal distribution has a mean of m = 70 with s = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 55?

0.8944

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

0.0668

What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%?

z = -0.52

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

0.0038

A normal distribution has a mean of m = 24 with s = 3. What is the minimum score needed to be in the top 14% of the distribution?

##### X = 27.24

If one score is randomly selected from a normal distribution with m = 100 and s = 20, the probability of obtaining a score between X = 80 and X = 120 is p = 0.3413.

False

What is measured by the numerator of the z-score test statistic?

The actual distance between M and mu

Which of the following accurately describes a hypothesis test?

An inferential technique that uses the data from a sample to draw inferences about a population

A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (H0) say about the treatment?

The treatment has no effect on the scores

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

#### z = 1.28

A vertical line drawn through a normal distribution at z = -1.00 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body?

0.8413

For a normal distribution, the proportion located between z = -1.00 and z = +1.00 is p = 34.13%

False

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

True

A normal distribution has a mean of m = 40 with s = 10. If a vertical line is drawn through the distribution at X = 35, what proportion of the scores are on the left side of the line?

##### 0.3085

A normal distribution has a mean of m = 70 with s = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 55?

0.8944

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

0.0668

What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%?

#### z = -0.52

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

0.0038

A normal distribution has a mean of m = 24 with s = 3. What is the minimum score needed to be in the top 14% of the distribution?

##### X = 27.24

For any normal distribution, the probability of randomly selecting a z-score less than z = 1.40 is p = 0.9192.

True

A normal distribution has a mean of m = 80 with s = 20. What score separates the highest 15% of the distribution from the rest of the scores?

##### X = 100.8

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

Proportions in both tails are less than 0.50.

A vertical line drawn through a normal distribution at z = -0.75 separates the distribution into two sections. The proportion in the smaller section is 0.2734.

True

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

0.4192

For a normal distribution with m = 100 and s = 20, the score that separates the top 60% of the distribution from the bottom 40% is X = 105.

False

For a normal distribution, the proportion located between z = -1.00 and z = +1.00 is p = 34.13%

False

For a hypothesis test evaluating the effect of a treatment on a population mean, what basic assumption is made concerning the treatment effect?

If there is a treatment effect, it will add/subtract a constant to each score

The critical boundaries for a hypothesis test are z=+1.96/-1.96. If the z-score for the sample data is z=-1.90, what is the correct statistical decision?

Fail to reject the null hypotheis

What z-score values form the boundaries for the middle 60% of a normal distribution?

#### z = +0.84 and z = -0.84

A vertical line is drawn through a normal distribution at z = 1.20. What proportion of the distribution is on the left-hand side of the line?

0.8849

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

True

A normal distribution has a mean of m = 80 with s = 20. What score separates the highest 40% of the distribution from the rest of the scores?

##### X = 85

A normal distribution has a mean of m = 100 with s = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 90 and X = 110?

0.3830

For a normal distribution with m = 50 and s = 10, the line separating the highest 10% of the scores from the rest is located at X = 51.28.

False

A vertical line drawn through a normal distribution at z = 1.40 divides the distribution into two sections. The proportion in the smaller section is 0.0808.

True

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

##### 0.8664

For a normal distribution, the proportion in the tail beyond z = -2.00 is equal to -0.0228.

False

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

False

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

All of the other 3 choices are correct.

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

False

A normal distribution has a mean of m = 70 with s = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 58?

0.8413

If one score is randomly selected from a normal distribution with m = 100 and s = 20, the probability of obtaining a score between X = 90 and X = 100 is p = 0.3085.

False

A vertical line is drawn through a normal distribution at z = 0.80. What proportion of the distribution is on the right-hand side of the line?

0.2119

Scores on the SAT form a normal distribution with a mean of m = 500 with s = 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?

##### X = 475

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?

10/40

A normal distribution has a mean of m = 100 with s = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 80 and X = 100?

0.3413

A normal distribution has a mean of m = 40 with s = 10. If a vertical line is drawn through the distribution at X = 55, what proportion of the scores are on the right side of the line?

0.0668

A vertical line drawn through a normal distribution at z = -1.00 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body?

0.8413

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

##### 0.2743

A normal distribution has a mean of m = 70 with s = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 55?

0.8944

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

0.0668

What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%?

##### z = -0.52

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

0.0038

A normal distribution has a mean of m = 24 with s = 3. What is the minimum score needed to be in the top 14% of the distribution?

##### X = 27.24

For a normal distribution with m = 50 and s = 10, the line separating the highest 10% of the scores from the rest is located at X = 51.28.

False

A vertical line drawn through a normal distribution at z = 1.40 divides the distribution into two sections. The proportion in the smaller section is 0.0808.

True

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

0.8664

For a normal distribution, the proportion in the tail beyond z = -2.00 is equal to -0.0228.

False

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

False

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

All of the other 3 choices are correct.

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

False

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