A graduate student who takes 3 courses in one semester If Xt

A graduate student who takes 3 courses in one semester. If X=the number of courses with grade \"A\". The random variable X has a probability distribution as follows

x

0

1

2

3

p(x)

0.1

0.15

0.65

0.1

The probability P(X < 2) is equal to?

0.90

0.25

0.15

0.65

Let Z represent a standard normal random variable. P(Z>0) is equal to?

0.0

0.5

0.45

0.9

Solution

1) P(X<2 ) = P(0,1) = 0.1 + 0.15 = 0.25

2) P(Z>0) = 0.5 because std. normal distribution is symmetric about its mean (zero).