Study Guide for Problem # 8 (original final review sheet)

Jenny Soriano

Problem 8:

The following is the probability distribution of Jeanette’s study hours for Mathematics in a given week.

 X   (hours) 2 4 5 6 P(X) 0.21 0.39 ? 0.15

a) Find the probability of X=5.

b) Find the mean of the probability distribution.

c) Find the standard deviation of the probability distribution.

a) The easiest way to find the probability of X=5 is adding all the other X’s and subtracting 1 from the answer. The result of the subtraction is the probability of X=5

Steps:

0.21+0.39+.15= .75 → 1-.75= .25 → P(5)= .25

Reason: The probability distribution p(X) should always equals 1 when you add                            them up.

b)      Find the mean of the probability distribution:

Steps: By making a probability distribution chart: ↓

 x P(x) xp(x) x² p(x) 2 0.21 .42 .84 4 0.39 1.56 6.24 5 0.25 1.25 6.25 6 0.15 .9 5.4 ∑(x)= 7 ∑p(x)= 1 ∑xp(x)=4.13 ∑ x²p(x)= 18.73

µ= mean/average

∑xp(x)= µ   µ= 4.13   µ²= 17.0569

To find the standard deviation, you have to use the formula: ∑ x²p(x) –  µ² ← has to be square rooted