13. What is the probability a randomly chosen SBU sophomore is either a female or from NY? (5 points)
This is an addition problem, using a union: P(F)+ P(NY) - P(OnNY) = .7+.5-.4=.8
14. If 55% of these SBU sophomores are either females or in engineering, then what is the probability that a randomly chosen sophomore is a female engineering major? (5 points)
We have 2 marginals and 1union, so we can find an intercept as well. P(F)+P(E) P(FnE) = P(FuE), .5 + .2 - x = .55, so X=.15
15. Show or explain whether being from NY and being a female are statistically independent events? (5 points)
We will test if P(F)*P(NY) = P(FnNY) so .5*.7 = .35 which does not equal to .4. Thus they are not independent.
Questions 16 refers to the following.
The probability distribution for X, the length of long-distance telephone calls in minutes is as follows:
X: time in minutes          5    10    15      20
P(X): probability             .20 .50    .20    .10
16. What is the expected value for the length of these calls? (5 points)
This requires us to use the expected value formula - so we sum value* "probability: 5°.2+10*.5+15*.2+20*.1=11.

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Solution 13
Increasing order is given below:

IQR = Q3...

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