Under what conditions can the binomial distribution be approximated by the Poisson? Let n be the number of trials, p be the probability of success on each trial, and q = 1 − p. (Select all that apply.) n ≥ 30 n ≥ 100 and np ≥ 10    n ≥ 100 and np < 10 np > 5 and nq > 5 np ≤ 5 and nq ≤ 5

Q: Suppose that x has a binomial distribution with n = 50 and p = 0.6, so that µ = np = 30 and o =…

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

Q: If no is greater than or equal to 5, estimate P(fewer than 5) with n=14 and P=0.5 by using the…

A:

Q: if np greater than or equals 5 and nq greater than or equals 5, estimate Upper P left parenthesis…

A: Given: n = 14, p = 0.4, q = (1 – p) = 1 – 0.4 = 0.6 Following conditions must be satisfied to use…

Q: If np is greater than/or = to 5 and nq is greater than/or = 5, Estimate P(fewer than 7) with n=13…

A:

Q: Assume that a procedure yields a binomial distribution with a trial repeated n=10n=10 times. Use…

A: It is given that n = 10, p = 0.51 and k = 2.

Q: Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some…

A: Solution: We are given that a random variable k follows a binomial distribution with n = 5 and…

Q: Suppose that a binomial experiment has n=5n=5 independent trials and the probability of success on a…

A: Solution: Let X be the random variable. From the given information, X follows binomial distribution…

Q: 8. Suppose that 20% of the articles produced by a machine are defective, the defectives occurring at…

A: Given p=probability of defective machine=20100=0.2 n= sample size=400 Let X be the number of…

Q: Suppose that a population is known to be normally distributed with μ = 2,000 and σ = 230. If a…

A:

Q: A fabric manufacturer believes that the proportion of orders for raw material arriving late is p =…

A: As given proportion of orders for new material arriving late is p=0.6 Null hypothesis is H0 : p=0.6…

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

A: Given that n= 500 , p=0.025 Here, we need to use normal approximation to a Binomial Distribution (X)…

Q: A fabric manufacturer believes that the proportion of orders for raw material arriving late is p =…

A: Given Information: Proportion of orders for raw material arriving late is p=0.6. Sample size n=10 If…

Q: Every day, patients arrive at the dentist’s office. If the Poisson distribution were applied to this…

A:

Q: If np 2 5 and nq 2 5, estimate P(more than 9) with n= 11 and p= 0.6 by using the normal distribution…

A:

Q: If np(is greater than or equal to)5, estimate P(fewer than 5) with n=13 and p=0.4 by using the…

A:

Q: Suppose that the random variable has the binomial distribution, X - B(100, 0.2) , and is the…

A: Here it is given that X~Bin(100,0.2) where n=100 and p=0.2.

Q: If np≥5 and nq≥5​, estimate P(fewer than 5) with n=13 and p=0.6 by using the normal distribution as…

A: np= 13×0.6=7.8&gt;5 nq=13×0.4=5.2&gt;5 We use normal approximation to calculate probability.

Q: Assume that a procedure yields a binomial distribution with a trial repeated n = 7 times. Find the…

A:

Q: Assume that a procedure yields a binomial distribution with a trial repeated n=10n=10 times. Use…

A:

Q: If np≥5 and nq≥5​, estimate P(fewer than 3) with n=13 and p=0.4 by using the normal distribution as…

A:

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 greater than or equals 5 and nq greater than or equals 5 ​, estimate P(fewer than 5) with n=…

A:

Q: If np is greater than or equal to 5 and nq is greater than or equal to 5, estimate P(fewer than 4)…

A:

Q: An automobile manufacturer finds that 1 in every 2000 automobiles produced has a particular…

A: a)It is given that n =5,500 and p = 1/2000.The probability mass function of binomial distribution is…

Q: Suppose that only 0.1% of all computers of a certain type experience CPU failure during the warranty…

A:

Q: If np≥5 and nq≥​5, estimate P(more than 6) with n=13 and p=0.3 by using the normal distribution…

A:

Q: If np ≥ 5 and nq ≥ 5​, estimate P(fewer than 2) with n=13 and p=0.4 by using the normal distribution…

A:

Q: I know the Poisson limit distribution can be used when n is large and p is small to represent a…

A: When the value of n is Binomial distribution is large and p -value is very small, then the binomial…

Q: Consider the corresponding zero-truncated Poisson distribution. Evaluate the probabilities p, for k…

A:

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

A:

Q: If the random variable X has a Poisson distribution where the lambda equals 7, Then the different…

A:

Q: Compute P(X) using the binomial probability formula. Then determine whether the normal distribution…

A: We have given that  n=40 , p=0.3 , X=15 Find  P(x=15)

Q: Suppose that X is a binomial random variable with n=200 and p=0.5 a.) Find the probability P(x is…

A: It is given that n=200 and p=0.5.

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

A: The normal dsitribution is generally a good approximation to the binomial distribution when np and…

Q: If np > or equal 5 and nq >equal 5, estimate P (fewer than 5) with n= 14 and P=0.5 by using the…

A:

Q: If np≥5 and np≥5​, estimate P(fewer than 5) with n=14 and p=0.6 by using the normal distribution as…

A: Given, n = 14 and p = 0.6 q = 1 - p = 1 - 0.6 = 0.4 np = 14*0.6 = 8.4 which is greater than 5 nq =…

Q: An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular…

A:

Q: a) Evaluate α assuming that p=0.6. Use the binomial distribution.   b) Evaluate β for the…

A: Given Information: Null and alternative hypothesis are, H0 : Proportion of college graduate students…

Q: If np greater than or equals 5 and nq greater than or equals 5 , estimate P(at least 9) with n= 13…

A: Summary of this question It np is greater than or equal to 5 and nq is greater than or equals 5.

Q: (1) Use the normal distribution to approximate the probability that there will be at least 17…

A: Given Information : Let r be the binomial random variable that represent the number of neutral…

Q: It is assumed that X has a Poisson distribution with some parameter A with A 20, but the value of A…

A:

Q: If np > 5 and nq > 5, estimate P(fewer than 2) with n = 13 and p = 0.4 by using the normal…

A: Given, n=13 and p=0.4 Therefore, Therefore, normal distribution as an approximation to the binomial…

Q: Is the success-failure condition of the Central Limit Theorem satisfied? A) No. Either np < 10 or…

A: p = 0.1 n = 279   a)Yes. Both np and n(1−p) are ≥10. b)The Central Limit Theorem tells us that the…

Q: Assume that a procedure yields a binomial distribution with a trial repeated n=9n=9 times. Find the…

A: From the provided information, Sample size (n) = 9 Probability of success (p) = 0.68 The process…

Q: If np≥5 and nq≥​5, estimate P(more than 8) with n=11 and p=0.3 by using the normal distribution…

A: Suppose, X follows Binomial distribution with parameters n and p. If np≥ 5 and nq≥5 q=1-p, then X…

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: If np is greater than 5 and nq is greater than 5, estimate P(at least 6) with n=13 and p=0.6 by…

A: Given information- p = 0.6 n = 13   So, np = 13 × 0.6 = 7.8 Which is greater than 5. And, nq = 13 ×…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.