# MATHEMATICS

25.The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 534 MPa with a standard deviation of 13 MPa.

(a)

What is the probability that a randomly chosen sample of glass will break at less than 534 MPa? (Round your answer to 2 decimal places.)

Probability

(b)

What is the probability that a randomly chosen sample of glass will break at more than 559 Mpa? (Round your answer to 4 decimal places.)

Probability

(c)

What is the probability that a randomly chosen sample of glass will break at less than 567 MPa? (Round your answer to 4 decimal places.)

Probability

26.Half of a set of the parts are manufactured by machine A and half by machine B. Five percent of all the parts are defective. Two percent of the parts manufactured on machine A are defective.

Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.)

Probability

27.A student’s grade on an examination was transformed to a z value of 0.67. Assuming a normal distribution, we know that she scored approximately in the top:

25 percent.

40 percent.

50 percent.

15 percent.

28.Which pairs of events are independent?

(a) P(A) = 0.28, P(B) = 0.14, P(A∩B) = 0.10.

A and B are

.

(b) P(A) = 0.15, P(B) = 0.48, P(A∩B) = 0.05.

A and B are

.

(c) P(A) = 0.80, P(B) = 0.10, P(A∩B) = 0.08.

A and B are

.

29.A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. The top 2.5 percent of the applicants would have a score of at least (choose the nearest integer):

646.

617.

606.

600.

30.A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive. The mean of this distribution is:

33.5.

32.5.

31.5.

30.5.