MAT/STA 325 Exam 1 - Statistics, Exams of Mathematics

The february 15, 2001 exam for mat/sta 325 statistics course. The exam includes questions on calculating means and standard deviations, probability theory, and independent events. Students are required to solve problems related to data analysis, foul shots, and purchasing defective items.

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Pre 2010

Uploaded on 08/09/2009

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MAT/STA 325 Exam 1 February 15, 2001
Prof. Thistleton
1. You are given the data shown on the accompanying graph.
(a) Calculate the mean of the data set.
(b) Calculate the standard deviation of the data set.
(c) Express the data point 4 in standard units.
Suppose you have a distribution with mean µ= 20 and standard deviation σ=5. Whatcan
you say about the proportion of data
(a) between 5 and 35?
(b) above 40?
01234567
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
class frequencies
class marks
1
pf3
pf4
pf5

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MAT/STA 325 Exam 1 February 15, 2001 Prof. Thistleton

  1. You are given the data shown on the accompanying graph.

(a) Calculate the mean of the data set.

(b) Calculate the standard deviation of the data set.

(c) Express the data point 4 in standard units.

Suppose you have a distribution with mean μ = 20 and standard deviation σ = 5. What can you say about the proportion of data

(a) between 5 and 35?

(b) above 40?

(^00 1 2 3 4 5 6 )

1

2

3

4

5

class frequencies

class marks

  1. After extensive analysis you have determined that, when you attempt two consecutive foul shots, the probability that you are successful on the first is 0.7 and the probability that you are successful on the second is 0.75. Also, the probability that you are successful on the second given that you miss the first is 0.35.

FIRST SECOND

I

II III IV

(a) State in words what each of the regions I, II, III, and IV represents.

(b) Calculate the probability of each of the regions I, II, III, and IV.

(c) What is the probability that you are successful on the second shot given that you are successful on the first shot?

  1. Suppose that 10% of items from a manufacturer are defective in some way. Suppose also that these items are defective independently of one another. You purchase 4 items.

(a) What is the probability of that you will obtain 0 defectives?

(b) What is the probability of that you will obtain 1 defectives?

(c) What is the probability of that you will obtain 2 defectives?

(d) What is the probability of that you will obtain 3 defectives?

(e) What is the probability of that you will obtain 4 defectives?

  1. A deck of cards has 52 cards, of which 13 are labeled Hearts, 13 are labeled Clubs, 13 are labeled Spades, and 13 are labeled Diamonds. You deal yourself 5 cards. Calculate the probability that you deal yourself

(a) 0 Hearts.

(b) 1 Heart.

(c) 2 Hearts.

(d) 3 Hearts.

(e) More that 3 Hearts.

(f) You will buy 4 lottery tickets. Each ticket is either a Win or a Loss. Draw a tree diagram showing all possible outcomes of this experiment.