Math Answers

A math teacher believes that a grade 7 student will get a score of not more than 70 in the 100-item diagnostic test administered last week. To test this claim, the scores of 40 students who took the diagnostic test was recorded. The mean of their scores is 87.65 with a standard deviation of 6. Which of the following test statistic should be used?

Perpetrators of a crime who have been given the maximum sentence of 10 years are believed by a fiscal to have been sentenced to more than 7 years on the average. A random sample of 20 of these crime offenders reveals a mean sentence of 7.6 years with a standard deviation of 2.4 years. Which of the following test statistic should be used?

Let P(x,y) be the statement "student x has taken a class y", where the domain for x consist of all students and y consist of all computer engineering courses/subject at your school .

- Expree each of the quantification in

English sentences.

• ∀x∀yP(x,y)

• ∀x∃yP(x,y)

• ∃x∀yP(x,y)

• ∃x∃yP(x,y)

If the mean and standard deviation of a continuous random variable that is normally distributed are 28 and 3 respectively using the empirical rule find an interval that contains 95% of the distribution

ACTIVITY #4

Scoring system: 1 point for correct answer and 2 points for the solution

A. Use the Table of Standard Normal distribution to determine corresponding probabilities of the following:

1. P(Z < -1.45)

2. P(0.5<Z < 2.33)

3. P(Z > 1.78)

B. X is a normally distributed random variable with a mean of 60 and a standard deviation of 8. Find the probabilities indicated by using the table.

1. P(X < 52)

2. P(48 < X < 64)

3. P(X > 57)

C. Solve the following problems by supplying the needed information.

The average number of calories in a 1.8-ounce chocolate bar is 230. Suppose that the distribution of calories is approximately normal with a standard deviation of 10.

1. Find the probability that a randomly selected chocolate bar will have less than 200 calories.

2. Find the probability that a randomly selected chocolate bar will have greater than 195 calories. 3. What is the percentage that a chocolate bar is randomly selected between 200 calories and 250 calories?

Activity #5

2. The scores of the 5 randomly selected HUMSS students are given below:

26

45

31

लल 34

34

44

47

23

44

38

Complete the table and compute for the sample mean, sample variance, and sample standard

deviation,

Student's No.

Scores (x)

2

3

4

3

£x =

Write your computations here

sample mean

sample variance

sample standard deviation

29

E = mc²

2x+5y+3z=2

x+2y+2z=4

x+y+4z=11. Use the elementary row reduction to solve for the linear system.

Confidence level=97%