Question

Asked Feb 18, 2019

Complete parts (a) and (b) below.

The number of dogs per household in a small town

Dogs

0

1

2

3

4

5

Probability

0.616

0.243

0.092

0.026

0.014

0.009

(a) Find the mean, variance, and standard deviation of the probability distribution.

Find the mean of the probability distribution.

Step 1

**a.**

**Find the average number of dogs per household in a small town using the given probability distribution.**

Consider the variable *X *be the number of dogs per household in a small town.

The data represents the number of dogs per household in a small town and the corresponding probabilities of the number of dogs per household in a small town.

*Mean:*

The general formula to obtain the expected value or mean of a discrete random variable is,

µ = *E*(*X*) = ∑*X*P*(*X*)

The mean of the variable *X *is obtained as **0.606** from the calculation given below:

Step 2

**Obtain the variance of the variable X using the given probability distribution.**

*Variance:*

The general formula to obtain the variance of a discrete random variable is,

*V*(*X*) = ∑*X*^{2}**P*(*X*) – (∑*X*P*(*X*))^{2}

The variance of the variable *X *is obtained as **0.9268** from the calculation given below:

Step 3

**Obtain the standard deviation of the variable X using the given probability distribution.**

*Standard deviation:*

The general formula to obtain the standard deviation of a discrete random variable is,

*S.D *(*X*) = SQRT(V(*X*)) = SQRT( ∑*X*2**P*(*X*) – (&s...

Tagged in

Q: Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flyi...

A: (a) Poisson distribution:It is a discrete probability distribution that models the number of events ...

Q: Simple random sampling uses a sample of size from a population of size to obtain data that can be us...

A: The population size is denoted by ‘N’ and the sample size is denoted by ‘n’.Let the number of differ...

Q: Which statement regarding skewed distributions is FALSE? The "68-95-99" rule does not apply to skew...

A: The 68-95-99 rule is applicable only in normal distributions. So it is not applicable to skewed dist...

Q: M Asigmnt Ose ook St hx Ch S g The D x4 ttp/ww.asignnet/wbudentsignment-Responses/subithdep-21213790...

A: Box and whisker plot:A type of graph used to display patterns of quantitative data is called a boxpl...

Q: Use the normal approximation to the binominal to approximate the probabilities. A gardener buys a pa...

A: Normal approximation to the binomial:If a random variable X ~ B(n, p) in which n is large and p is c...

Q: Select the statistic test that best fits each description. Study exploring the relationship between ...

A: Introduction:A brief introduction to the various tests suggested here is given below:T-test independ...

Q: 3.It is thought that basketball teams that make too many fouls in a game tend to lose the game even ...

A: (a) The value of coefficient of determination:The given data is represented in the following table:

Q: A research group claims that 20% of patients with dementia never develop full Alzheimer's. In a simp...

A: According to the given question, to test the hypothesis that the research group claims that 20% of p...

Q: How do I run a the test of normality? Assumptions of normality

A: Introduction:Several tests of normality exist, using which you can verify whether a particular data ...