Statistics and Probability Answers

A. Answer the following. Solution is required.

A call center agent in a BPO company has received an average of 15 calls per hour.

a. What is the probability that he will receive 7 calls from 3am to 3:30am? Determine also its mean and variance. (15 points)

b. What is the probability that he will receive atleast 6 calls for a period of 1 hour? (10 points

c. What is the probability that he will receive atleast 8 calls, but not more than 12 calls in a span of 1 and a half hour? (10 points)

B. Give atleast three (3) real-life applications (each) of Binomial distribution and Poisson distribution. (15 points)

1.You play a game with two six-sided dice. If you roll a sum of 4 or 7, you win P 400. If you roll a sum of 10,you win 200. However, you lose 300 for anything else. If you continue to play the game, how much do you expect to win or lose in the game?

A. Four coins are tossed. Let X be the random variable representing the number of heads that occur. Find the values of the random variable X.

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 strenght is 390 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 two - tailed with a = 0.01

The average pre-school cost for tuition fees last year was Php. 17,250. The following year 20 institutions had a sample mean of Php. 16,150 and a standard deviation of Php. 2,250. At 0.90 level of confidence is there sufficient evidence to conclude that the mean cost has increased?

For a continuous random variable that has a normal distribution with mean of 24 and a standard deviation of 6, find the area under the normal curve from 𝑥=18 and 𝑥=21.

A population and = 6 consists of the following values: 12, 14, 16, 18, 20 and 22. Estimate the population mean by using a sampling distribution with a random variable of size n= 3. Prepare and analyze the probability distributions of the sample means of the population values of N = 6.

Suppose that the relation consists of the scores of 6 students in a certain examination as follows 9, 11, 13, 15, 17 and 19 using the sampling distribution is to make the population mean using a random variable of the size n = 2.

Let X be a random variable with pdf

𝑓(𝑥) = {

2(1 + 𝑥)

27 𝑖𝑓 2 ≤ 𝑥 ≤ 5

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Find (i) 𝑃(𝑋 < 4) (ii) 𝑃(3 < 𝑥 ≤ 4)

The density function of sheer strength of spot welds is given by

𝑓(𝑥) = {

𝑥/ 160000 𝑓𝑜𝑟 0 ≤ 𝑥 ≤ 400

800 − 𝑥/ 160000 𝑓𝑜𝑟 400 ≤ 𝑥 ≤ 800

Find the number a such that 𝑃(𝑋 < 𝑎) = 0.50

student is to match three historical events (Mahatma Gandhi’s Birthday, India’s freedom, 

and First World War) with three years (1947, 1914, 1896). If he guesses with no knowledge 

of the correct answers, what is the probability of the number of answers he gets correctly?