Search
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%
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.
Let S = {w1,w2,...,wk} be a basis for the vector space V. Prove that every vector in V can
be expressed as a linear combination of vectors w1,w2,...,wk
in exactly one .
