Statistics and Probability Answers

Below is a 5-item true or false test. Determine whether the statement is true or

false. Write T if the statement is true and F if false on the blank provided before the

number.

1. The area under a normal curve is 100.

2. The area under the curve corresponds to all probabilities of X.

3. The mean of a standard normal curve is 0.

4. The normal curve is bell-shaped and is symmetrical about its center.

5. The curve is determined by the standard deviation of the distribution.

Before you proceed and explore more about the normal curve, let us see how

much you know before we tackle the lesson. Determine whether each of the following 

statements is true or false. Write T if the statement is correct and write F if not.

1. Percentile rank is the percent of cases that are at or below a score.

2. 90thpercentile means that 90% of the grades were higher than yours and

10% were lower.

3. The 90th percentile under the normal curve is z = 1.28.

4. The upper 5% of the normal curve is above z = 0.56.

5. The 95th percentile under the normal curve is 𝑧 = 1.60

Solve the problem below.

The average monthly salary for a newly hired teacher in a private school is P18,000. If the hiring salary at this school is normally distributed with a standard deviation of P3,000, what is the probability that a newly hired employee randomly selected from a list receives a monthly salary which is less than P15,000?

Write your solution here:

Determine the area corresponding to the following z-scores.

1. greater than 𝑧 = 2.31

2. less than 𝑧 = 1.20

3. between 𝑧 = −1.96 and 𝑧 = 2

Before you proceed and explore on computing probabilities under the normal

curve, let us see how much you know before we tackle the lesson. Below is a 5-item

true or false test. Determine whether the statement is true or false. Write T if the

statement is true and F if false on the blank provided before each number.

1. Probability value is a number from 0 to 1.

2. Probability value is a number from −1 to 1.

3. Finding the area of a region is the same as finding the probability

associated with that region.

4. The probability that the z-score falls at most 𝑧 = −1 is equal to the

probability of that the z-score falls less than 𝑧 = −1.

5. It is possible to have a negative probability.

1. Given 𝑥 = 60; and 𝑠 = 6, find the z-score that corresponds to each of the following

scores up to two decimal places.

a. 𝑥 = 70

b. 𝑥 = 58

2. Given 𝜇 = 72; and 𝜎 = 8, find the z-score that corresponds to each of the following

scores up to two decimal places.

a. 𝑥 = 68

b. 𝑥 = 80

3. Alex scored 90 during the first periodic exam in Mathematics and 88 during the

second periodic exam. The scores in first periodic exam have a mean 𝜇 = 83 and

a standard deviation 𝜎 =9. Scores in the second periodic exam have a mean 𝜇 =

80 and a standard deviation 𝜎 = 8. In which periodic exam was his standing better,

assuming that the scores in his periodic exams are normally distributed?

4. On a final examination in Biology, the mean was 75 and the standard deviation

was 12. Determine the standard score of a student who received a score of 60

assuming that the scores are normally distributed.

5. Given: 𝜇 = 64,𝜎 = 7. What is the raw score when 𝑧 = −0.76?

Find each of the following percentile points and draw the appropriate normal

curve. Complete your procedures.

1. Find the 99th percentile of the normal curve.

2. Find the upper 5% of the normal curve.

3. The results of the entrance examination for freshmen are normally distributed

with 𝑥 = 85 and 𝑠 = 12.5. What is the percentile rank of a score of 92?

Find the probabilities of the following.

1. 𝑃(𝑧 > 1.36)

2. 𝑃(𝑧 < 2.45)

3. 𝑃(1.2 < 𝑧 < 1.4)

4. 𝑃(−2.75 < 𝑧 < −0.56)

5. 𝑃(𝑧 > −1.05)

Find the area under the normal curve in each of the following cases.

1. to the right of𝑧 = 1.63

2. between 𝑧 = −1.36 and 𝑧 = 2.55

3. to the left of𝑧 = −1.78

4. between 𝑧 = −2.76 and 𝑧 = −1.25

5. between 𝑧 = 1.56 and 𝑧 = 2.51

Using the z-table, find the corresponding area between 𝑧 = 0

and each of the following:

1. z = 0.92

2. z = 1.29

3. z = 2.73

4. z = −0.50

5. z = −2.98