1686 words - 7 pages

Final Exam

Review Questions

You should work each of the following on your own, then

review the solutions guide. DO NOT look at the solutions guide

first.

1. Determine whether the following are nominal, ordinal, interval, and ratio.

a. Daily temperatures in Ripon, WI

b. Test scores in statistics class

Solution: (a) would be interval as there is no zero while (b) would be ratio as there is a zero.

2. The following numbers represent the weights in pounds of six 7-year old children in Mrs. Jones' 2nd grade class. {25, 60, 51, 47, 49, 45} Find the mean; median; mode; variance; standard deviation.

Solution: This would be a sample from the class

mean = 46.166 ...view middle of the document...

Interpret the results of r2 value.

Solution:

(a) yˆ= 859 + 5.76*3200 + 3.82*3000

= 859 + 18432 + 11460

= 30751 which is 30,751,000 pounds of rice

(b) 94% of the variation in the annual rice yield can be explained by the number of acres planted and harvested. The remaining 6% is unexplained and is due to other factors or to chance.

7. The Student Services office did a survey of 500 students with the following results:

| Transfer | Non-transfer | Total |

Part-time | 100 | 110 | 210 |

Full-time | 170 | 120 | 290 |

Total | 270 | 230 | 500 |

e. Find the probabilities that a student is a transfer student.

f. Find the probability that a students is part-time.

g. Find the probability that a student is a transfer student and a part-time student

h. Find the probability that a student is a transfer student, given that the student is part-time, P(transfer|part-time).

Solution: (a) The total number of transfer students is 270. The total number of students in the survey is 500. P(Transfer) = 270/500 = .54 (b) The total number of part time students is 210. The total number of students in the survey is 500. P(Part Time) = 210/500 = .42 (c) From the table we see that there are 100 students which are both transfer and part time. This is out of 500 students in the sample. So, 100/500 = .20 (d) This is conditional probability and so we must change the denominator to the total of what has already happened. There are 100 students which are both transfer and part time. There are 210 part time students. P(transfer | part time) = 100/210 ≈ .4762.

8. A shipment of 40 television sets contains 3 defective units. How many ways can a vending company can buy five of these units and receive no defective units?

Solution: There are 37 sets which are not defective. There are 37C5 ways to get 5 sets with none defective. 37C5 = 435, 897. In Excel, it would be =COMBIN(37,5). Thus, there are 435,897 ways to get 5 sets with non-defective.

9. A company claims that 61% of consumers know about their product. If the company asks 18 consumers, what is the probability that (a) exactly 10 will say yes, that (b) between 10 and 12 will say yes.

Solution: For part A, it would be =BINOM.DIST(10,18,0.61,FALSE) to get 0.167 or 16.7%. For part B, it would be =BINOM.DIST(12,18,0.61,TRUE)- BINOM.DIST(10,18,0.61,TRUE) to get 0.3634 or about 36%.

10. The mean number of cars per minute going through the Eisenhower turnpike automatic toll is about 7. Find the probability that exactly 3 will go through in a given minute.

Solution: =poisson.dist(3,7,FALSE) to get 0.0521 or about 5%.

11. On a dry surface, the braking distance (in meters) of a certain car is a normal distribution with mu = μ = 45.1 m and sigma = σ = 0.5

i. Find the braking distance that represents the 91st percentile.

j. Find the probability that the braking distance is less than or equal to 45 m

k. Find the probability that the...

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