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 ? .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.

Answers

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

the answer is…1.29

 

 

 

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