Skip to main content

Use the binomial distributaccuracy of the normal approximatbinomial distribution. n=20, pi=5a. Compute the exact probabilities and corresponding normal approximations for y < 5.b. The normal approximation can be improved slightly by taking P(y ≤ 4.5). Why should this help? Compare your results.c. Compute the exact probabilities and corresponding normal approximation with the continuity correction for P(8 < y < 14).

Question
100%

Use the binomial distributaccuracy of the normal approximat
binomial distribution. n=20, pi=5
a. Compute the exact probabilities and corresponding normal approximations for y < 5.
b. The normal approximation can be improved slightly by taking P(y ≤ 4.5). Why should this help? Compare your results.
c. Compute the exact probabilities and corresponding normal approximation with the continuity correction for P(8 < y < 14).

Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
Not helpful? See similar books
MATLAB: An Introduction with Applications
Learn more about
Estimation
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Statistics Q&A

Find answers to questions asked by students like you.

Q: Suppose that X has a Poisson distribution with h = 80. Find the probability P (X<70) based on the…

A: As per our guidelines, we are allowed to answer first question only. Thanks   1) X has Poisson…

Q: Let Xhave a binomial distribution with parameters n = 25 and p=.4. Calculate P (9 < X < 12) using…

A: X have a binomial distribution with parameter n=25 and p=0.4 By using normal approximation…

Q: for the binomial distribution with n=24 and p=0.6, state whether or not it is suitable to use the…

A: Click to see the answer

Q: For a binomial distribution with parameters n=25 and p=0.70, determine the continuity correction for…

A: We have to find continuity correction for given data.

Q: For a binomial distribution with n=8 and P=0.5, find P=(3≤X≤6) and P(X=4) using the normal…

A: Click to see the answer

Q: Suppose that X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. Find the…

A: Given,  X has a hypergeometric distribution with N = 2,000, K = 800, and n = 200. We have to find…

Q: Suppose that X has a hypergeometric distribution with N = 2,000, K= 800, and n= 200. Find the…

A: Click to see the answer

Q: Suppose that X has a hypergeometric distribution with N = 2,000, K= 800, and n= 200. Find the…

A: Click to see the answer

Q: S. Suppose that X has a Poisson distribution with h= 80. Find the probability P(X< 70) based on the…

A: given: random variable x follow Poisson distribution with parameter h=80  Then to find probability…

Q: Suppose that X-bin(75,0.2). Using the normal approximation to the binomial distribution, P(14.< X <…

A: Given,n=75p=0.2mean(μ)=np=75×0.2=15standard deviation(σ)=np(1-p)σ=75×0.2×0.8σ=3.4641

Q: Suppose that X-bin(65,0.2). Using the normal approximation to the binomial distribution, P(12. < X…

A: Click to see the answer

Q: Suppose X1, . . . , Xn are i.i.d. from a Poisson distribution with parameter λ, which is unknown.…

A: Given that: x1,x2..xn from a Poisson distribution with parameter λ

Q: Suppose that X-bin(75,0.2). Using the normal approximation to the binomial distribution P(14 < X <…

A: Given,n=75p=0.2mean(μ)=np=75×0.2=15standard deviation(σ)=np(1-p)σ=75×0.2×1-0.2σ=3.4641

Q: The moment generating function of the negative binomial distribution is given by pe' m, ()=1-ge 1-…

A: Click to see the answer

Q: If the probability of defective bolts is 0.1, find (a) the mean and standard deviation for the…

A: Click to see the answer

Q: Suppose that X-bin(65,0.2). Using the normal approximation to the binomial distribution, P(12.< X <…

A: Click to see the answer

Q: If np ≥ 5 and nq ≥ 5​, estimate P(fewer than 4 ) with n=11 and p-0.7 by using the normal…

A: Obtain the probability that fewer than 4.   The probability that fewer than 4 is obtained below as…

Q: The moment generating function of the negative binomial distribution is given by pe' my (t) =| 1-…

A: Click to see the answer

Q: Q3) Let X.X2X,*be a random sample from the truncated exponential Je x20 distribution with pdf:…

A: Click to see the answer

Q: Suppose that X~bin(75,0.2). Using the normal approximation to the binomial distribution, P(14.< X <=…

A: GivenX~Binomial(75,0.2)

Q: f np≥5 and nq≥​5, estimate P(more than 8) with n=14 and p=0.7 by using the normal distribution…

A: Given n=14 and p=0.7

Q: If np ≥ 5 and nq ≥ 5, estimate P(fewer than 5) with n =14 and p=0.4 y using the normal…

A: Normal approximation to the binomial: From the given information, sample size, n = 14. The…

Q: Suppose that X has a hypergeometric distribution with N = 1000, k = 600 and n=200. Find the…

A: Click to see the answer

Q: Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: Click to see the answer

Q: Estimate​ P(6) for n=18 and p=0.3 by using the normal distribution as an approximation to the…

A: According to the provided information, n=18 p=0.3   The pmf of the binomial distribution,   P(X=x) =…

Q: Estimate​ P(6) for n=18 and p=0.3 by using the normal distribution as an approximation to the…

A: Given that, Sample size, n = 18 Probability, p = 0.3

Q: Let X, , X, be a random sample from a Normal distribution with mean u and variance a. Given that the…

A: Hello! As you have posted 4 different questions, we are answering the first question. In case you…

Q: Use binomial formula to-find P (X = 17) - Use normal distribution to approximate P (X=17) %3D

A: Given that X follows Binoimal(n = 25, p = 0.50)

Q: Use the Suppose in a local Kindergarten through 12th grade (K -12) school district, 53% of the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: According to the answering guidelines, we can answer only three subparts of a question and the rest…

Q: Suppose that we want to use the normal approximation to the binomial distribution to determine b(1;…

A: Click to see the answer

Q: (i) Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: Given data: Sample size (n)  =500 Probability (p) = 0.025 Here we have to use; normal approximation…

Q: If np is greater than or equal to 5 and nq is greater than or equal to 5, estimate P(at least 7) n…

A: Given,          n=13          P=0.6    and q=1-p           q=1-0.6=0.4       nP=13×0.6=7.8⩾5…

Q: The Project Manager found that distribution of the amount of gravel (in tons) sold by a particular…

A: Given: X is a random variable of the amount of gravel (in tons) sold. The probability distribution…

Q: H9. Using the Monte Carlo method, find the critical value (T) of a normal distribution such that…

A: Click to see the answer

Q: For a Gaussian distribution function, f(x) = a exp[- (x- m)<], where a and mare positive constants.…

A: Given information: The probability density function of a Gaussian distribution is as given below:…

Q: Recall that for use of a normal distribution as an approximation to the binomial distribution, the…

A: If the binomial distribution approximated to normal distribution the following  conditions needs to…

Q: Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: Click to see the answer

Q: Let the random variable X fit the exponential distribution with the parameter λ. Find the…

A: Solution: From the given information, X follows exponential distribution with parameter λ.

Q: If np > 5 and nq 2 5, estimate P(more than 9) withn = 13 and p = 0.6 by using the normal…

A: Given Data sample size,n= 13 probability of success,p= 0.6 probability of…

Q: Using the Binomial distribution with n = 5 and p = 0.3, calculate %3D P(x at most 3) = [three…

A: Binominal distribution

Q: Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: From the provided information, Sample size (n) = 500 and p = 0.025

Q: Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population…

A: In question, Given that in a local kindergarten through 12th grade school district 49% population…

Q: Find the probability Pr⁡( Z ≤ 2.054 ) using the Standard Normal distribution (μ=0, σ=1).

A: Required probability is P(Z≤2.054)

Q: A researcher found that a cigarette smoker smokes on average 30 cigarettes a day. She feels that…

A: Given: x¯ = 29 n = 9 s = 2.3 α = 0.05

Q: Find the right critical value for the F-distribution when a = .05 and DFN = 6 and DFD = 10

A: Here, DFN denotes the Degrees of freedom for numerator . DFD denotes the degrees of freedom for…

Q: For the binomial distribution P(x) = C7x(0.4) (0.6)' -X, choose the correct histogram below and…

A: Binomial distribution is the standard form of the binomial distribution. In binomial distribution…

Q: The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be…

A: Introduction: Denote π as the true population proportion. It is given that π = 2% = 0.02. Denote p…

Q: If np 25 and nq 2 5, estimate P(at least 2) with n= 13 and p 0.4 by using the normal distribution as…

A: Given n=13 P=0.4

Q: The number of clients a store has during a week is Poisson distributed with mean A = 25. The amount…

A: The moment generating function is, ϕt=e1000t+250t2 Mean: Et=ddtϕt   by putting t=0…

Knowledge Booster
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • MATLAB: An Introduction with Applications
    Statistics
    ISBN:9781119256830
    Author:Amos Gilat
    Publisher:John Wiley & Sons Inc
    Probability and Statistics for Engineering and th...
    Statistics
    ISBN:9781305251809
    Author:Jay L. Devore
    Publisher:Cengage Learning
    Statistics for The Behavioral Sciences (MindTap C...
    Statistics
    ISBN:9781305504912
    Author:Frederick J Gravetter, Larry B. Wallnau
    Publisher:Cengage Learning
  • Elementary Statistics: Picturing the World (7th E...
    Statistics
    ISBN:9780134683416
    Author:Ron Larson, Betsy Farber
    Publisher:PEARSON
    The Basic Practice of Statistics
    Statistics
    ISBN:9781319042578
    Author:David S. Moore, William I. Notz, Michael A. Fligner
    Publisher:W. H. Freeman
    Introduction to the Practice of Statistics
    Statistics
    ISBN:9781319013387
    Author:David S. Moore, George P. McCabe, Bruce A. Craig
    Publisher:W. H. Freeman
  • MATLAB: An Introduction with Applications
    Statistics
    ISBN:9781119256830
    Author:Amos Gilat
    Publisher:John Wiley & Sons Inc
    Probability and Statistics for Engineering and th...
    Statistics
    ISBN:9781305251809
    Author:Jay L. Devore
    Publisher:Cengage Learning
    Statistics for The Behavioral Sciences (MindTap C...
    Statistics
    ISBN:9781305504912
    Author:Frederick J Gravetter, Larry B. Wallnau
    Publisher:Cengage Learning
    Elementary Statistics: Picturing the World (7th E...
    Statistics
    ISBN:9780134683416
    Author:Ron Larson, Betsy Farber
    Publisher:PEARSON
    The Basic Practice of Statistics
    Statistics
    ISBN:9781319042578
    Author:David S. Moore, William I. Notz, Michael A. Fligner
    Publisher:W. H. Freeman
    Introduction to the Practice of Statistics
    Statistics
    ISBN:9781319013387
    Author:David S. Moore, George P. McCabe, Bruce A. Craig
    Publisher:W. H. Freeman