Statistics and Probability Answers

A division wide aptitude test in mathematics was conducted to 1000 pupils. The mean of the test is 58 and the standard deviation is 12. The scores also approximate the normal distribution. What is the minimum score to belong the upper 20% of the group?

1. Directions: Determine each of the following areas and show these graphically. Use probability notation in your final answer. NOTE: Use graphing paper to graph.

1. To the left of z = 1.96 5. Below z = -1.96       9. 1.27≥z≥-2.1

2. At most z = 2.58 6. z≥1       10. z=-0.58

3. At least z = 1.96 7. z≤-1.5

4. To the right of z = 0.33 8. -0.92≤z≤1.75

For a two-tailed test with variance unknown, n=19, and a=0.05, what is the critical value?

The value that separates a rejection region from an acceptance region is called a

In a right-trailed test with a = 0.01. the critical value of z is

Find 𝑝̂𝑎𝑛𝑑 𝑞̂, given X and n.

1. X = 56, n = 80

B. Find the finite population correction factor given the following: 1. 𝑁=150 𝑛=15 2. 𝑁=600 𝑛=35 

1. Solve the problems below. Show your solutions completely.

1. Find the 95th percentile of a normal curve.

2. Find the upper 10% of the normal curve.

3. Where does the 50th percentile lie under the normal curve?

4. A teacher mark the performance of the students in terms of their relative standing in class. Find the z values that corresponds to each of the given information.

Mary Anne – 93% Agnes – 50% Edith – 78%

Roland – 81% Kyle – 96%

5. The results of a nationwide aptitude test in Math are normally distributed with m = 80 and s =15. What is the percentile rank of a score of 84?

2000 Grade 11 students of DNHS took a Statistics test. The scores were distributed normally with a mean of 70 and Standard deviation of 10. Label the mean and three standard deviation from the mean.

1. What percentage of scores are between 70 and 80?

2. What percentage of scores are between 60 and 80?

3. What percentage of scores less than a score of 60?