Question

The normal approximation of the binomial distribution is appropriate when np ≥ 5. n(1 − p)...

The normal approximation of the binomial distribution is appropriate when

np ≥ 5.

n(1 − p) ≥ 5.

np ≤ 5.

n(1 − p) ≤ 5 and np ≤ 5.

np ≥ 5 and n(1 − p) ≥ 5.

Homework Answers

Answer #1

np ≥ 5 and n(1 − p) ≥ 5.

By using some mathematics it can be shown that there are a few conditions that we need to use a normal approximation to the binomial distribution. The number of observations n must be large enough, and the value of p so that both np and n(1 - p) are greater than or equal to 5. This is a rule of thumb, which is guided by statistical practice. The normal approximation can always be used, but if these conditions are not met then the approximation may not be that good of an approximation.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The normal approximation of the binomial distribution is appropriate when: A. np 10 B. n(1–p) 10...
The normal approximation of the binomial distribution is appropriate when: A. np 10 B. n(1–p) 10 C. np ≤ 10 D. np(1–p) ≤ 10 E. np 10 and n(1–p) 10
If np≥5 and nq≥5​, estimate P(fewer than 6) with n=13 and p=0.6 by using the normal...
If np≥5 and nq≥5​, estimate P(fewer than 6) with n=13 and p=0.6 by using the normal distribution as an approximation to the binomial​ distribution; if np<5 or nq<​5, then state that the normal approximation is not suitable.
1. Normal Approximation to Binomial Assume n = 10, p = 0.1. a. Use the Binomial...
1. Normal Approximation to Binomial Assume n = 10, p = 0.1. a. Use the Binomial Probability function to compute the P(X = 2) b. Use the Normal Probability distribution to approximate the P(X = 2) c. Are the answers the same? If not, why?
Suppose that x has a binomial distribution with n = 202 and p = 0.47. (Round...
Suppose that x has a binomial distribution with n = 202 and p = 0.47. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (σ) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x np n(1 – p) Both np and n(1 – p) (Click to select)≥≤ 5 (b)...
Suppose that x has a binomial distribution with n = 199 and p = 0.47. (Round...
Suppose that x has a binomial distribution with n = 199 and p = 0.47. (Round np and n(1-p) answers to 2 decimal places. Round your answers to 4 decimal places. Round z values to 2 decimal places. Round the intermediate value (σ) to 4 decimal places.) (a) Show that the normal approximation to the binomial can appropriately be used to calculate probabilities about x. np n(1 – p) Both np and n(1 – p) (Click to select) 5 (b)...
5) If it is appropriate to do so, use the normal approximation to the  p^-distribution to calculate...
5) If it is appropriate to do so, use the normal approximation to the  p^-distribution to calculate the indicated probability: n=60,p=0.40n=60,p=0.40 P( p̂  < 0.50)= ? Enter 0 if it is not appropriate to do so.
If np greater than or equals 5(np≥5) and nq greater than or equals 5(nq≥5​), estimate P(fewer...
If np greater than or equals 5(np≥5) and nq greater than or equals 5(nq≥5​), estimate P(fewer than 4) with nequals=13 and p equals=0.5 by using the normal distribution as an approximation to the binomial​ distribution; if np<5 or nq<​5, then state that the normal approximation is not suitable.
A binomial distribution has p? = 0.26 and n? = 76. Use the normal approximation to...
A binomial distribution has p? = 0.26 and n? = 76. Use the normal approximation to the binomial distribution to answer parts ?(a) through ?(d) below. ?a) What are the mean and standard deviation for this? distribution? ?b) What is the probability of exactly 15 ?successes? ?c) What is the probability of 14 to 23 ?successes? ?d) What is the probability of 11 to 18 ?successes
Suppose X is binomial random variable with n = 18 and p = 0.5. Since np...
Suppose X is binomial random variable with n = 18 and p = 0.5. Since np ≥ 5 and n(1−p) ≥ 5, please use binomial distribution to find the exact probabilities and their normal approximations. In case you don’t remember the formula, for a binomial random variable X ∼ Binomial(n, p), P(X = x) = n! x!(n−x)!p x (1 − p) n−x . (a) P(X = 14). (b) P(X ≥ 1).
Normal Approximation to Binomial Assume n = 100, p = 0.4. Use the Binomial Probability function...
Normal Approximation to Binomial Assume n = 100, p = 0.4. Use the Binomial Probability function to compute the P(X = 40) Use the Normal Probability distribution to approximate the P(X = 40) Are the answers the same? If not, why?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • In your travels or readings, what branding strategies, activities or identifiers have major U.S. brands altered...
    asked 14 minutes ago
  • Find the mean of the data summarized in the given frequency distribution. Compare the computed mean...
    asked 14 minutes ago
  • Prove that √3 is irrational. You may use the fact that n2 is divisible by 3...
    asked 16 minutes ago
  • You are the vice president of a 60-bed cardiac hospital. Last year your hospital generated about...
    asked 21 minutes ago
  • A company has an 11% WACC and is considering two mutually exclusive investments (that cannot be...
    asked 24 minutes ago
  • Century National Bank has offices in several cities in the Midwest and the southeastern part of...
    asked 35 minutes ago
  • Constructivist learning approaches and techniques ALL emphasize Select one: a. school based learning activities b. group...
    asked 1 hour ago
  • 9.1.5 Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger...
    asked 1 hour ago
  • A simple pendulum with a length of 2.73 m and a mass of 6.54 kg is...
    asked 1 hour ago
  • Step 3: Complete the following chart by writing what the counter and the totalNumbers value stores...
    asked 1 hour ago
  • The difference between Independent-measures ANOVA and Repeated-measures ANOVA is that the variance estimates for the Repeated-measures...
    asked 1 hour ago
  • Use Pinterest to find a picture for each that best illustrates intrapersonal intelligence and interpersonal intelligence...
    asked 1 hour ago