Statistics and Probability Answers

Consider the following information P(A)=0.25 P(Bc)=0.40 and P(A and B)=0.08,Then P(A|B)is 0.2

A population consists of 1, 5, 6, 8, 12, 7, and 11. Suppose a sample of size 3. Find the 

mean and variance.

2. The scores of individual students on a national test have a normal distribution with mean of 18.6 and a standard deviation of 5.9. At Federico Ramos Rural High School, 76 students took the test. If the scores at this school have the same distribution as national scores, solve for the following:

a. determine the mean and standard deviation of the sampling distribution of the sample mean.

b. find the probability that the sample mean falls between 17 and 20 (𝑃(17 < 𝑥̅< 20).

c. the number of sample means that is above 19.3 kilograms.

1. A population consists of six values (6, 9, 12, 15, 18, and 21).

a. Select a random sample of size 3. Explain the random sampling that you used.

b. How many possible samples can be drawn?

c. List all possible samples and compute the mean of each sample.

d. Construct a frequency distribution of the sample means obtained in step 2 including 𝑥̅; 𝑓; 𝑃(𝑥̅); ̅𝑥 ⋅ 𝑃(𝑥̅); ̅𝑥 2 ⋅ 𝑃(𝑥̅); Σ𝑃(𝑥̅); Σ𝑥̅⋅ 𝑃(𝑥̅) 𝑎𝑛𝑑 Σ𝑥̅ 2 ⋅ 𝑃(𝑥̅).

2.) Scores on the SAT form a normal distribution with a mean score of 500 and a standard deviation of 100.

a. What is the minimum score necessary to be in the top 15% of the SAT distribution?

b. Find the range of scores that defines the middle 80% of the distribution of SAT scores.

3. )The government would like to conduct a subsidy program for the lowest 5 percent of the families in terms of income. The government gathered data about family income and it’s found to be normally distributed with a mean of Php 130 000 and a standard deviation of Php 50 000. What is the cutoff income for the government program?

1.) In a National Achievement Test, the mean was found to be 75 and the standard deviation was 15. The scores also approximate the normal distribution.

a. What is the minimum score that belongs to the upper 15% of the group?

b. What is the two extreme scores outside of which 15% of the group are expected to fall?

c. What is the score that divide the distribution into two such that 75% of the cases below it?

d. Estimate the range of scores that will include the middle 45% of the distribution.