UNIT TEST 2 - SP11

Who is credited with the development of the Normal Distribution?

• Carl Fridriech Gauss

• Carl Friedriech Gauss

• Carl Fredrich Gauss

• Carl Friedrich Gauss

What is the formula to get 2 standard deviations below the mean?

• σ-2μ

• 2σ-μ

• -2σ+μ

• -2σ-μ

Using the empirical rule, how many probabilities are there outside of three standard deviations from the mean?

• 0.3%

• 4.6%

• 0.03%

• 1.3%

Arrange the process on how to get the area whether on the left or right of the given z-score.

I. Identify the region under the normal curve by drawing a vertical line through the given 𝑍 value.

II. Sketch the standard normal distribution.

III. Shade the required region.

IV. Use the 𝑍 table to determine the area associated with the given 𝑍 value.

• I, II, III, IV

• II, III, I, IV

• II, I, III, IV

• IV, I, II, III

Which of the following statements is true regarding the probability density function (PDF)?

• It can take on negative values.

• It directly gives the probability of a random variable.

• The total area under the PDF curve is always equal to 1.

• It is only applicable to discrete random variables.

A researcher is examining the scores of students on a difficult exam. If the distribution of scores is negatively skewed, what does this indicate about the performance of the students?

• Most students performed better than average on the exam.

• Most students performed worse than average on the exam.

• The performance of students is consistent across all score ranges.

• The scores are evenly distributed across all students.

If a student scores in the 75th percentile on a standardized test, what does this mean?

• The student answered 75% of the questions correctly.

• The student's score is lower than 75% of the other students who took the test.

• The student's score is higher than 75% of the other students who took the test.

• The student's score is exactly at the 75th mark.

Find the area under the standard normal curve on the right of 2.20

• 98.61%

• 1.39%

• 10.39%

• 1.36%

Find the area between z=-2.55 and z=2.27.

• 9.83%

• 98.30%

• -98.30%

• 99.38%

Assume that a set of test scores is normally distributed with a mean of 82 and a standard deviation of 8. Compute the three standard deviations below the mean.

• 106

• 90

• 74

• 58