Math Answers

The probability density function of a continuous random variable X is given below:

𝑓(𝑥) = {

1.25(1 − 𝑥

4

) , 0 < 𝑥 < 1

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

a. Find P(0.4< X<0.9)

b. Compute the expected value and variance of X.

Draw Dienes block to show how to find the solution to 78 + 56

If A and B are any two events defined on a sample space S with the following probabilities:   P(A)=0.44, P(B)=0.70, and P(A∩B)=0.44. Then, P(A∪B) is

2. Determine the truth value of each of these statements if the domain consist of all integers.

A. ∀n (n+1>n)

B. Ǝn (n = -n)

C. Ǝn (2n = 3n)

D. ∀n (3n ≤ 4n)

To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from

1. Let Q(x) denote the statement “x is an integer”. What are the truth values?

A. Q(-1)

B. Q(0)

C. Q(8/2)

D. Q(sqrt(-4))

E. Q(sqrt(4))

Bag A contains 10 marbles of which 2 are red and 8 are black. Bag B contains 12 marbles of which 4 are red and 8 are black. A ball is drawn at random from each bag.

a) Draw a probability tree diagram to show all the outcomes the experiment.

b) find the probability that:

i. Both are red

ii. Both are black

iii) one black and one red

iv) at least one red

To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from

In a class of 40 students 15 grew cabbage 10 lettuce 5 both Cabbage and lettuce the rest neither calculate the probability that a randomly selected from class grew cabbage

1. The average number of milligrams (mg) of cholesterol in a cup of a certain brand of ice cream is 660 mg, the standard deviation is 35 mg. Assume the variable is normally distributed.

a. If a cup of ice cream is selected, what is the probability that the cholesterol content will be more than 670 mg?

b. If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg?

2.In a study of the life expectancy of 400 people in a certain geographic region, the mean age at death was 70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that the mean life expectancy will be less than 68 years?