Statistics and Probability 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?

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

Confidence level=97%

Two dice are thrown. What is the probability that the first die rolls a 1 if it is known that the number of points on the second die is higher than on the first?

From a pocket containing 10 coins (20 cents each) and 10 coins (3 cents each), 10 coins are taken randomly. What is the probability that the amount of money left in the pocket is not less than the one taken out

The multiple-choice question on a combinatorics quiz contains 20 questions with ten possible answers each (where only 1 answer is true). Compute the probability of randomly guessing the correct answers and getting at least 10 correct answers to 20 questions (Event A). Find the mathematical expectation and variance of the number of correct answers.

Two boxes, 1 and 2 are given. Suppose box 1 contains 6 black and 7 white balls. Box 2 contains 9 black and 8 white balls. Three balls are selected at random from box 1 and put into box 2. Then two balls are selected at random from box 2.

1) what is the probability that these two balls have the same color

2) what is the probability that these two balls have the different colors