1. Compute f (12).

2. Compute f (16).

3. Compute

Irvin Dukes
2021-12-16
Answered

Consider a binomial experiment with $n=20\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}p=.70$ .

1. Compute f (12).

2. Compute f (16).

3. Compute$P(x\ge 16)$ .

1. Compute f (12).

2. Compute f (16).

3. Compute

You can still ask an expert for help

Heather Fulton

Answered 2021-12-17
Author has **31** answers

Step 1

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”

(1) Compute f (12).

The value of the function f (12) is obtained below:

Let X denotes the random variable which follows binomial distribution with the probability of success 0.70 with the number trails 20.

That is, \(\displaystyle{n}={12},{p}={0.70},{q}={0.30}{\left(={1}-{0.70}\right)}\)

The probability distribution is given by,

\[P(X=x)=(\begin{array}{c}n\\ x\end{array})p^{x}(1-p)^{n-x};\ here\ x=0,1,2,...,n\ for\ 0 \le p \le 1\]

Where n is the number of trials and p is the probability of success for each trial.

The required probability is,

\(\displaystyle{f{{\left({12}\right)}}}={P}{\left({X}\le{12}\right)}\)

Use Excel to obtain the probability value for x equals 12.

Follow the instruction to obtain the P-value:

1. Open EXCEL

2. Go to Formula bar.

3. In formula bar enter the function as“=BINOMDIST”

4. Enter the number of success as 12.

5. Enter the Trails as 20

6. Enter the probability as 0.70

7. Enter the cumulative as True.

8. Click enter

EXCEL output:

From the Excel output, the P-value is 0.2277

Thus, the value of the function f (12) is 0.2277.

Step 2

2. Compute f (16).

The value of the function f (16) is obtained below:

The required probability is,

\(\displaystyle{f{{\left({16}\right)}}}={P}{\left({X}\le{16}\right)}\)

Use Excel to obtain the probability value for x equals 16.

Follow the instruction to obtain the P-value:

1. Open EXCEL

2. Go to Formula bar.

3. In formula bar enter the function as“=BINOMDIST”

4. Enter the number of success as 16.

5. Enter the Trails as 20

6. Enter the probability as 0.70

7. Enter the cumulative as True.

8. Click enter

EXCEL output:

From the Excel output, the P-value is 0.8929

Thus, the value of the function f (16) is 0.8929.

Step 3

(3) Compute the probability \(\displaystyle{P}{\left({x}\geq{16}\right)}\).

The probability \(\displaystyle{P}{\left({x}\geq{16}\right)}\) is obtained below as follows:

The required probability is,

\(\displaystyle{P}{\left({x}\geq{16}\right)}={1}-{P}{\left({x}{ < }{16}\right)}\)

\(\displaystyle={1}-{P}{\left({x}\le{15}\right)}\)

Use Excel to obtain the probability value for x equals 15.

Follow the instruction to obtain the P-value:

1.Open EXCEL

2. Go to Formula bar.

3. In formula bar enter the function as“=BINOMDIST”

4. Enter the number of success as 15.

5. Enter the Trails as 20

6. Enter the probability as 0.70

7. Enter the cumulative as True.

8. Click enter

EXCEL output:

From the Excel output, the P-value is 0.7625.

\(\displaystyle{P}{\left({x}\geq{16}\right)}={1}-{P}{\left({x}{ < }{16}\right)}\)

\(\displaystyle={1}-{P}{\left({x}\le{15}\right)}\)

\(\displaystyle={1}-{0.7625}\)

\(\displaystyle={0.2375}\)

The probability \(\displaystyle{P}{\left({x}\geq{16}\right)}\ {i}{s}\ {0.2375}\).

Neil Dismukes

Answered 2021-12-18
Author has **37** answers

Step 1

Given:

$p=0.70$

$n=20$

Formula binomial probability:

$$f(k)=(\begin{array}{c}n\\ k\end{array})\times {p}^{k}\times (1-p{)}^{n-k}$$

a)$$f(12)=(\begin{array}{c}20\\ 12\end{array})\times {0.70}^{12}\times (1-0.70{)}^{20-12}=0.114397$$

b)$$f(16)=(\begin{array}{c}20\\ 16\end{array})\times {0.70}^{16}\times (1-0.70{)}^{20-16}=0.130421$$

c) Add the corresponding probabilities:

$P(X\ge 16)=f\left(16\right)+f\left(17\right)+f\left(18\right)+f\left(19\right)+f\left(20\right)=0.2375$

d) Use the complement rule for probabilities:

$P(X\le 15)=1-P(X\ge 16)=1-0.2375=0.7625$

Step 2

e) The mean of a binomial distribution is the sample size n and the probability p:

$\mu =np=20\times 0.70=14$

f) The standard deviation of a binomial distribution is the square root of the product of the sample size n and the probabilities p and q. The variance is the square of the standard deviation.

${\sigma}^{2}=npq=np(1-p)=20\left(0.70\right)(1-0.70)=4.2$

$\sigma =\sqrt{npq}=\sqrt{np(1-p)}=\sqrt{20\left(0.70\right)(1-0.70)}\approx 2..0494$

Given:

Formula binomial probability:

a)

b)

c) Add the corresponding probabilities:

d) Use the complement rule for probabilities:

Step 2

e) The mean of a binomial distribution is the sample size n and the probability p:

f) The standard deviation of a binomial distribution is the square root of the product of the sample size n and the probabilities p and q. The variance is the square of the standard deviation.

Jeffrey Jordon

Answered 2021-12-27
Author has **2027** answers

Step 1

Given that

a)

b)

c)

=1-0.7643(Using Binomial Table)

d)

e)

f)

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