Math Answers

EXERCISE 2: Find the rank and the nullity of the linear transformation S: p_1→ℝ given by 

     S(p(x)) = ∫_0^1p(x)dx.

Direction: Answer the following and illustrate each under the normal curve:

1. Compute the probability area to the left of z = -1.25.

2. Compute the probability area above z = 1.

3. Find the probability area between z = -0.25 and z = 1.5.

4. Find the 90th percentile of a normal curve.

5. Compute the upper 5% of the normal curve.

The following sample observations were randomly selected:

X. 4. 5. 3. 6. 10

Y. 4. 6. 5. 7. 7

determine the correlation coefficient and the coefficient of determination

Check whether the series sum_(n=1)^(oo)(nx)/(n^(4)+x^(3)) x in 0 alpha is uniformly convergent or not

2. In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is MPa. The decision for the extension of the contract with the manufacturer depends on the engineer . Test the hypothesis whether there is no significant difference between the two means using a twotailed with a = 0.01

1. A meeting of envoys was attended by 4 koreans and 2 filipinos. If there envoys were selected at random one after the other , determine the values of the random variable F representing the number of Filipinos.

2. During a sale at a men’s store, 16 white sweaters, 3 red sweaters, 9 blue sweaters, and 7 yellow sweaters were purchased. If a customer is selected at random, find the probability that he bought,

a. A blue sweater. (3 marks)

b. A yellow or a white sweater. (3 marks)

c. A red, blue or a yellow sweater. (3 marks)

d. A sweater that was not white (3 marks)

In a science test, the mean score is 42 and the standard deviation is 5. Assuming the scores are normally distributed, what percent of the score is greater than 47

Calculate the circumference of a circle with a diameter of 1.2mm

In a company having 180 employees, 60 earn $10.00 per hour and 120 earn $12.00 per hour. 30 employees each earns $12.00 leave the work. Determine the mean earnings per hour.