For the binomial distribution with n = 10 and p = 0.4, where p is probability...

For the binomial distribution with n = 10 and p = 0.4, where p is probability of success. Let X be the number of successes.

(a) Find the probability of three or more successes.

(b) Find the µ, E(X), and σ 2 , V ar(X)

Expert Solution

TOPIC:Binomial distribution.

orchestra answered 3 years ago

Assume the binomial distribution is appropriate. If N = 10 and P = 0.30, the probability...

Assume the binomial distribution is appropriate. If N = 10 and P = 0.30, the probability of getting at least 8 P events is _________.

If P=0.4% and n =600. Is the poison distribution a reasonable approximation distribution of the binomial...

If P=0.4% and n =600. Is the poison distribution a reasonable approximation distribution of the binomial distribution? Yes or No What is the mean of this binomial distribution ( and the mean of poison distribution used to approximate it) Mean= What is the actual mean of this binomial distribution Standard deviation (actual)= What is the mean of the approximate poison distribution? Standard deviation approximate Are these values in reasonable agreement

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n=80, p=0.4

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n=80, p=0.4 The mean, μ, is _______ (Round to the nearest tenth as needed.) The variance, σ2, is _______ (Round to the nearest tenth as needed.) The standard deviation, σ, is _______ (Round to the nearest tenth as needed.)

A binomial probability distribution has p = 0.25 and n = 81. A) What are the...

A binomial probability distribution has p = 0.25 and n = 81. A) What are the mean and standard deviation? B) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. C) What is the probability of exactly 28 successes? D) What is the probability of 18 to 22 successes? E)What is the probability of 24 or fewer successes?

Assume a binomial probability distribution has p = 0.70 and n = 300.

Assume a binomial probability distribution has p = 0.70 and n = 300. (a) What are the mean and standard deviation? (Round your answers to two decimal places.) mean Incorrect: Your answer is incorrect. standard deviation Incorrect: Your answer is incorrect. (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. Yes, because np ≥ 5 and n(1 − p) ≥ 5. Yes, because n ≥ 30. No, because np < 5...

Assume a binomial probability distribution has p = 0.70 and n = 400.

Assume a binomial probability distribution has p = 0.70 and n = 400. (a) What are the mean and standard deviation? (Round your answers to two decimal places.) mean= standard deviation = (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. Yes, because np ≥ 5 and n(1 − p) ≥ 5. Yes, because n ≥ 30. Yes, because np < 5 and n(1 − p) < 5. No, because...

For a binomial probability distribution, n = 130 and p = 0.60. Let x be the...

For a binomial probability distribution, n = 130 and p = 0.60. Let x be the number of successes in 130 trials. a. Find the mean and standard deviation of this binomial distribution. a. Find the mean and the standard deviation of this binomial distribution. b. Find to 4 decimal places P(x ≤ 75) using the normal approximation. P(x ≤ 75) = c. Find to 4 decimal places P(67 ≤ x ≤ 72) using the normal approximation. P(67 ≤ x...

In a binomial distribution n = 10 and p = 0.30. Find the probabilities of the...

In a binomial distribution n = 10 and p = 0.30. Find the probabilities of the following events: (Round the final answers to 3 decimal places.) a. x = 2. Probability b. x ≤ 2 (the probability that x is equal to or less than 2). Probability c. x ≥ 3 (the probability that x is equal to or greater than 3). Probability

Assume a binomial probability distribution has p = 0.60 and n = 300. (a) What are...

Assume a binomial probability distribution has p = 0.60 and n = 300. (a) What are the mean and standard deviation? (Round your answers to two decimal places.) mean standard deviation (b) Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. No, because np ≥ 5 and n(1 − p) ≥ 5. Yes, because n ≥ 30. Yes, because np ≥ 5 and n(1 − p) ≥ 5. No, because np <...

Suppose that X is a single observation from a Binomial(n, p) distribution where n is known...

Suppose that X is a single observation from a Binomial(n, p) distribution where n is known and 0 < p < 1 is unknown. Consider three estimators of p: pˆ = X /n “sample proportion” pˆA = (X + 2)/ (n + 4) “plus four estimator” pˆB = (X + (√n/4))/( n + √ n ). “constant MSE estimator” (a) Find the bias functions for all three estimators. (b) Find the variance functions of all three estimators. (c) Find the...

Question