Various Algebra Problems to Solve

Can you give me the step by step solutions for the following problems?

14. A die is tossed 120 times. Find the probability of getting the following results.

Fewer than twenty-two 6's

18. A company is taking a survey to find out whether people like its product. Their last survey indicated that 70% of the population like the product. Based on that, of a sample of 58 people, find the probabilities of the following.

a. All 58 like the product.
b. From 28 to 30 (inclusive) like the product.

26. The blood types B- and AB- are the rarest of the eight human blood types, representing 1.5% and .6% of the population, respectively.

a. If the blood types of a random sample of 1000 blood donors are recorded, what is the probability that 10 or more of the samples are AB-?

b. If the blood types of a random sample of 1000 blood donors are recorded, what is the probability that 20 to 40 inclusive of the samples are B-?

c. If a particular city had a blood drive in which 500 people gave blood and 3% of the donations were B-, would we have reason to believe that this town has a higher than normal number of donors who are B-?

32. A professor gives a test with 100 true-false questions. If 60 or more correct is necessary to pass, what is the probability that a student will pas by random guessing?

The grading system known as "grading on the curve" is based on the assumption that grades are often distributed according to the normal curve, and that a certain percent of a class should receive each grade, regardless of the performance of the class as a whole. The following is how one professor might grade on the curve.

(See attached file #52)

What percentage of the students receive the following grades?

51. A
52. B
53. C