Questions may look more...But They are easy

1. The following data set is the distribution of BMIs of 50 students at UTA . Convert the frequency histogram to a probability distribution. (a) What is the probability that a student had a BMI of at least 27? (b) What is the probability that a student is not considered overweight, assuming that a BMI of below 22 is not considered overweight? BMI 12-16 17-21 22-26 27-31 31-35 36-40 Number 8 11 9 10 7 5 2. . A computer consulting firm presently has bids out on three projects. Let A, = {awarded project i}, for i = 1, 2, 3, and suppose that P(A,) = .22, P(A2) = .25, P(A3) = .28, P(A, n A,) = .11, P(A, n A,) = .05, P(A2 n A3) = .07, P(A, n A, n A3) = .01. Express in words each of the fol- Find the followings a. P(A2 A,) b. P(A, n A3 | A,) C. P(A2 U A3 | A,) d. P(A, n A2 n A, | A, UA, UA3). 3. A certain system can experience three different types of defects. Let A; (i=1,2,3) denote the event that the system has a defect of type i. Suppose that P(A,) = 0.12 P(A2) = 0.07 P(A3) = 0.05 P(A, U A2) = 0.13 P(A, U A3) = 0.14 P(A2 UA;) = 0.1 P(A, n A2 n A3) = 0.01 a. What is the probability that the system does not have a type 1 defect? b. What is the probability that the system has both type 1 and type 2 defects? c. Given that the system has a type 1 defect, what is the probability that is has a type 2 defect