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Exam 1 in STA 100: Probability and Statistics - Prof. William Thistleton, Exams of Data Analysis & Statistical Methods

State University of New York Polytechnic - Utica-RomeData Analysis & Statistical Methods
Prof. William Thistleton

Exam 1 for the sta 100 course on probability and statistics, held on october 2, 2003. The exam covers various topics such as evaluating expressions, calculating probabilities, mean and standard deviation, and interpreting histograms.

Typology: Exams

Pre 2010

Uploaded on 08/09/2009

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STA 100 Exam 1 October 2, 2003
Prof. Thistleton
1. Evaluate the following expressions:
10C5
12P5
5!
3
i=0
(i3)
2. Suppose a license plate consists of a sequence of 3 digits {0, 1, 2, ...,9 }followed by a
sequence of 3 letters {A, B, C, ...Z }. How many distinct licence plates can you make?
3. Suppose rather that a license plate consists of a sequence of 4 digits followed by a sequence
of 3 letters. How many distinct licence plates can you make?
1
pf3
pf4
pf5

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STA 100 Exam 1 October 2, 2003 Prof. Thistleton

  1. Evaluate the following expressions:

10 C 5

12 P 5

∑^3 i=

(i^3 )

  1. Suppose a license plate consists of a sequence of 3 digits { 0, 1, 2,... ,9 } followed by a sequence of 3 letters { A, B, C,... Z }. How many distinct licence plates can you make?
  2. Suppose rather that a license plate consists of a sequence of 4 digits followed by a sequence of 3 letters. How many distinct licence plates can you make?
  1. In a large group of students there are 200 men and 250 women. 10% of the men play an extracurricular sport, as do 8% of the women. Fill in the following table.

men women total play a sport don′t play a sport total

(a) What is the probability that a randomly selected student plays a sport?

(b) What is the probability that a randomly selected athlete is a woman?

  1. You regularly visit a certain pizza parlor and notice upon your many visits that the probability the cook is wearing a sports hat is 0.8. The probability that he is wearing sneakers is 0.6. Also, the probability that he is wearing a sports hat and sneakers is 0.5.

(a) What is the probability that he is wearing a sports hat or sneakers?

(b) What is the probability that he is not wearing a sports hat and is not wearing sneakers?

(c) What is the probability that he is wearing a sports hat given that he is wearing sneakers?

  1. Suppose you have a distribution with mean μ = 50 and variance σ^2 = 16. What can you say about the proportion of data

(a) between 42 and 58?

(b) below 38?

  1. You are attempting penalty kicks in soccer and have noticed that you are successful 80% of the time, independently from trial to trial. Suppose you attempt 4 kicks.

(a) What is the probability that you will be successful on 2 of them?

(b) What is the probability that you will be successful on 1 or more of them?

  1. You will toss a biased (unfair) coin 2 times.

(a) How many elements are in your sample space? List these elements.

(b) Fill in the following table if the probability of Heads is 0.4.

number of heads 0 1 2 probability

(c) Calculate the expected number of heads on 2 tosses.

  1. extra credit +5 There are 52 cards in a normal deck. You select 5 cards at random and without replacement. What is the probability that in your sample you obtain

(a) No Hearts?

(b) One Heart?

(c) Two or more Hearts?