   Chapter 9.1, Problem 27E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Mean, Variance, and Standard Deviation In Exercises 27 and 28, find the mean, variance, and standard deviation of the discrete random variable x. See Examples 4, 5, and 6.Spinner A spinner is divided into three equal sections labeled 1, 2. and 3. x is (a) the number landed on when the spinner is spun once and (b) the sum of the numbers landed on when the spinner is spun twice.

(a)

To determine

To calculate: The mean, variance and standard deviation of the discrete random variable x where x is the number landed on spinner when the spinner is spun once.

Explanation

Given Information:

A spinner is divided into three equal sections named 1, 2, 3.

Formula used:

Probability distribution:

The probability of a random variable x is

P(x)=Frequency of xNumber of outcomes in S=n(x)n(S)

Expected value:

If y is a discrete random variable with values y1,y2,,yn then the mean μ of the distribution is the expected value of y given by

E(y)=y1P(y1)+y2P(y2)++ynP(yn)

Where the expected value of y is denoted by E(y).

Variance:

Consider a random variable whose possible values are {x1,x2,x3,,xm} with a mean of μ. Then, the variance of the random variable is,

V(x)=(x1μ)2P(x1)+(x2μ)2P(x2)++(xmμ)2P(xm)

Standard deviation:

The standard deviation of the random variable is

σ=V(x)

Calculation:

A spinner is divided into three equal sections named 1, 2, 3.

Let S be the sample space. Then, S={1,2,3}.

So, a number of possible outcomes is 3.

The frequency of each possible outcome is,

Random variable,x123Frequency of x, n(x)111

So, the probability that 1 land on when the spinner is spun once is,

P(1)=Frequency of 1Number of outcomes in S=n(1)n(S)=13

The probability that 2 land on when the spinner is spun once is,

P(2)=Frequency of 2Number of outcomes in S=n(2)n(S)=

(b)

To determine

To calculate: The mean, variance and standard deviation of the discrete random variable x where x is the sum of the numbers landed on spinner when the spinner is spun twice.

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