Statistics and Probability Answers

The results of the nationwide aptitude test in mathematics are normally distributed with a mean of 80 and a standard deviation of 15. Find the raw score such that 70% of the cases are below it.

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.

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

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

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?

Average college cost of tuition fee for all private institutions last year was P 36,400. A random sample of costs this year for 45 institutions of higher learning indicated that the sample mean was P 37,900 and sample standard deviation was P 5,600. At the 0.10 level of significance, is there sufficient evidence t0 conclude that the cost has increased?

A report in LTO stated that the average age of taxis in the Philippines is 9 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 8.2 years. The o if the population is 2.3 years. At a = 0.05, can it be concluded that the average age of the taxis in his company is less than the national average?

A box contains (𝑥+1) red marbles, (2𝑥+4) yellow marbles, and (4𝑥−6) green marbles

(i)

Find an expression, in terms of 𝑥, for the total number of marbles in the box.

(ii)

A marble is drawn at random from the box. Write down an expression, in terms of 𝑥, for the probability that the marble is red.

(iii)

Given that probability in part (ii) is 1/5, find the value of 𝑥.