a.
To determine: the probability model for X.
X | 0 | 1 | 2 | 3 | 4 |
P(X) | 0.0625 | 0.25 | 0.375 | 0.25 | 0.0625 |
Given information:
The possible values of X is
Concept Used:
Binomial probability Distribution:
Consider a simple event with these properties:
Each trial has two possible outcomes, called success and failure.
The probability of success on each trial is the same. (We denote the probability of success as
The trials are independent.
If the binomial random variable
Calculation:
The probability of getting a head on a coin toss is
Substitute
Similarly, calculate the probability of getting
X | 0 | 1 | 2 | 3 | 4 |
P(X) | 0.0625 | 0.25 | 0.375 | 0.25 | 0.0625 |
b.
To determine: the expected value.
The expected value is 2.
Given information:
The possible values of X is
Concept Used:
Expected Value of a Discrete Random Variable:
The weighted mean of all possible values of a discrete random variable is called its expected values.
It is the sum of the products of all possible values and their probability.
Calculation:
X | 0 | 1 | 2 | 3 | 4 |
P(X) | 0.0625 | 0.25 | 0.375 | 0.25 | 0.0625 |
c.
To explain: the standard deviation of the number of heads.
The standard deviation is 1.
Given information:
The possible values of X is
Calculation:
The square root of the expected value of squared deviations from the mean,
Substitute all the values in
d.
To verify: the same value of
The values of
Given information:
X | 0 | 1 | 2 | 3 | 4 |
P(X) | 0.0625 | 0.25 | 0.375 | 0.25 | 0.0625 |
Concept Used:
Expected Value for a Binomial Distribution:
If the binomial random variable
Standard Deviation for a Binomial Distribution:
If the binomial random variable
Calculation:
The sample size
Chapter 10 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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