ACT 1

1. Prepare a probability distribution then find the mean, variance and standard deviation for the courses completed by the students in a certain college. Course Number of Students (X) Tourism 285 HRM 460 Business Administration 152 Mass Communication 185 Architecture and Engineering 98 Total 1,180 2. Results of a study conducted to determine the water consumptions in number of cubic meters of households in a subdivision along with the corresponding probabilities are show below. Find the mean, variance and standard deviation. Number of 48 50 52 54 56 cubic meters (X) Probability P(X) 0.25 0.30 0.18 0.15 0.12 3. The number of inquiries received per day by the Office of Admissions in a certain university is shown below. Find the mean, variance and standard deviation. (15 pts) Number of 22 23 24 25 26 27 Inquiries (X) Probability 0.08 0.19 0.36 0.25 0.07 0.05 P(X) X . P(X) X2 . P(X)1. Suppose the current annual salary of all teachers in the Philippines have a normal distribution with a mean of 95,000 pesos and a standard deviation of 20,000 pesos. (14 pts) a. Find the probability that the annual salary of a randomly selected teacher would be between 56,000 and 76,000. (with illustration, 6 pts) b. Find the probability that the annual salary of a randomly selected teacher would be at least 50,000 pesos. (with illustration, 4 pts) c. Find the probability that the annual salary of a randomly selected teacher would be 126,000 pesos. (with illustration, 4 pts) 2. Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council's GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 506 and a standard deviation of 96. (14 pts) a. What is the probability of an individual scoring above 520? (with illustration, 6 pts) b. What is the probability of an individual scoring below 506? (with illustration, 4 pts) c. What is the probability of an individual scoring from 387 to 712? (with illustration, 4 pts) 3. Given # = 45, and o = 5.5. (7 points) a. What is the raw score when z = -1.57? b. What is the raw score when z = 2.09? c. What is the raw score when -0.48