### 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**