Question

Answer all of the questions in order. Show all of your work. No credit will be given for correct answers with no work shown. Partial credit will be awarded where possible. Good luck.

1. A teacher has taken attendance of her class of five students for the entire semester and found the number of days with each level of attendance. Her records show the following:

                                     # of Students attending class: 1      2      3     4      5

Days in the semester with this attendance level (out of 30 days):            4      2     10    4     10

a) What’s the probability of there being 3 or more students on any random day?

b) What is the expected number of students to attend a randomly selected day?

2. On average, 30% of textile shipments from ABC Shipping Company are late.

a) What is the probability that less than three of the next 4 shipments will be late?

b) What is the probability that exactly 4 of the next 10 shipments will be late?

3. The average rate of “set waves”, larger waves which come in a small group and are preferred by surfers, is 8 per 20 min.

a) What is the standard deviation of the number of waves per 20 min?

b) What is the probability of there being 18 waves in an hour?

4. The height of maple trees are distributed normally with a mean of 31 meters and a standard deviation of 4 meters.

a) What is the probability of a tree being taller than 33 meters? Represent this graphically as well as numerically.

b) A group of 20 trees is selected at random. What is the probability that the average height of these 20 trees is more than 33 meters? Represent this graphically as well as numerically.

c) A group of 20 trees is selected at random. What is the probability that the average height of these trees is between 30 and 32 meters? Represent this graphically as well as numerically.

5. A pitcher pitches a strike ( a good pitch) an average of 75% of the time. What is the probability that in a given game, at least 77 pitches of 110 thrown were strikes? Represent this graphically as well as numerically.

Answer 1