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# A Discussion On Probability Distributions

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6. A coin is tossed 4 times. Let X denote the number of heads which appear in 4 tosses.
a) Construct a probability distribution for X
b) Find P(X>2)
c) Find the expected value of X
d) Find the variance and standard deviation of X

7. The probability that a randomly selected elementary or secondary school teacher from a city is female is 0.68, holds a second job is 0.38, and is female and holds a second job is 0.29. Find the probability that an elementary or secondary school teacher selected at random from this city is female or holds a second job.

8. Suppose the statistic final exam has 10 multiple choice questions, each with 4 choices. If a student randomly guesses the answers, what is the probability he will pass the final exam. (Assume the student passes with 60 or higher, and each question is worth 10)

##### Solution Summary

Here we solve some problems related to binomial distribution (probability for obtaining different cases, mean, SD) in coin toss and in multiple choice questions, and an example of combined probability.

##### Solution Preview

6. a.
Probability distribution,
P(X = r) = C(n,r) p^r q^(n-r)

p = 1/2 = 0.5, q = 1/2 = 0.5, n = 4

P(X=r) = C(4,r)*0.5^r * 0.5^(4-r) --Answer

b.
P(X >=2) = 1 - P(X<2) =
= 1 - P(X=0) - P(X=1)
= 1 - C(4,0)*p^0 * q^4 - C(4,1)*p^1 * q^3
= 1 - 1*1*0.5^4 - 4*0.5^1*0.5^3 = 0.6875 ...

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• MSc , Pune University, India
• PhD (IP), Pune University, India
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##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.