Consider a binomial experiment with n=20 and p=.70. 1. Compute f (12). 2. Compute f (16). 3. Compute P(x≥16).

Question

Consider a binomial experiment with n=20 and p=.70.  1. Compute f (12).  2. Compute f (16).  3. Compute P(x≥16).

Heather Fulton · Accepted Answer

Step 1Since 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,&amp;nbsp;n=12,p=0.70,q=0.30=1-0.70The probability distribution is given by,P(X=x)=(nx)px(1-p)n-x;&amp;nbsp;here&amp;nbsp;x=0,1,2,...,n&amp;nbsp;for&amp;nbsp;0≤p≤1Where n is the number of trials and p is the probability of success for each trial.The required probability is,f12=PX≤12Use Excel to obtain the probability value for x equals 12.Follow the instruction to obtain the P-value:1. Open EXCEL2. 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 206. Enter the probability as 0.707. Enter the cumulative as True.8. Click enterEXCEL output:From the Excel output, the P-value is 0.2277Thus, the value of the function f (12) is 0.2277.Step 22. Compute f (16).The value of the function f (16) is obtained below:The required probability is,f16=PX≤16Use Excel to obtain the probability value for x equals 16.Follow the instruction to obtain the P-value:1. Open EXCEL2. 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 206. Enter the probability as 0.707. Enter the cumulative as True.8. Click enterEXCEL output:From the Excel output, the P-value is 0.8929Thus, the value of the function f (16) is 0.8929.Step 3(3) Compute the probability&amp;nbsp;Px≥16.The probability&amp;nbsp;Px≥16&amp;nbsp;is obtained below as follows:The required probability is,Px≥16=1-Px&amp;lt;16=1-Px≤15Use Excel to obtain the probability value for x equals 15.Follow the instruction to obtain the P-value:1.Open EXCEL2. 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 206. Enter the probability as 0.707. Enter the cumulative as True.8. Click enterEXCEL output:From the Excel output, the P-value is 0.7625.Px≥16=1-Px&amp;lt;16=1-Px≤15=1-0.7625=0.2375The probability&amp;nbsp;Px≥16&amp;nbsp;is&amp;nbsp;0.2375.

Neil Dismukes · Accepted Answer

Step 1  Given:  p=0.70  n=20  Formula binomial probability:  f(k)=(nk)×pk×(1−p)n−k  a) f(12)=(2012)×0.7012×(1−0.70)20−12=0.114397  b) f(16)=(2016)×0.7016×(1−0.70)20−16=0.130421  c) Add the corresponding probabilities:  P(X≥16)=f(16)+f(17)+f(18)+f(19)+f(20)=0.2375  d) Use the complement rule for probabilities:  P(X≤15)=1−P(X≥16)=1−0.2375=0.7625  Step 2  e) The mean of a binomial distribution is the sample size n and the probability p:  μ=np=20×0.70=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.  σ2=npq=np(1−p)=20(0.70)(1−0.70)=4.2  σ=npq=np(1−p)=20(0.70)(1−0.70)≈2..0494

Jeffrey Jordon · Accepted Answer

Step 1 Given that X∼Binomial(n=20, p=0.7) a) F(x)∴P(x)=nCxPx(1−P)n−x =n!(n−x)!x!Px(1−P)n−x ∴F(13)=20C13(0.7)13(1−0.7)20−13 =20!7!13!(0.7)13(1−0.7)7 F(13)=0.1642 b) F(16)=P(x=16)=20C16(0.7)16(1−0.7)20−16 =20!16!4!(0.7)16(1−0.7)4 F(16)=0.1304 c) P(X≥16)=1−P(x&amp;lt;16) =1−P(X≤15) =1-0.7643(Using Binomial Table) P(X≥16)=0.2357 d) P(X≤15)=P(x=0)+P(x=1)+P(x=2)+P(x=3) +P(x=4)+P(x=5)+P(x=6)+P(x=7)+P(x=8) +P(x=9)+P(x=10)+P(x=11)+P(x=12) +P(x=13)+P(x=14)+P(x=15) =0+0+0+0 +0+0+0.0002+0.0010+0.0039 +0.120+0.308+0.0554+0.1144 +0.1643+0.1916+0.1789 P(X≤15)=0.7643 e) F(x)=np ∵X∼B(np) =20×0.7 F(x)=14 f) var(x)=npq ∵q=1−p =20×0.7(1−0.7) var(x)4.2 σ=var(x)=2.04

Consider a binomial experiment with n = 20\ and\ p

Answered question

Answer & Explanation

New Questions in High school probability