In this problem, given the parameters n=3 and p=0.35, (a) construct the corresponding binomial probability distribution;...

In this problem, given the parameters n=3 and p=0.35, (a) construct the corresponding binomial probability distribution; (b) compute the mean and standard deviation of this distribution using the formulation that works for any discrete random variable; (c) compute the mean and standard deviation of this distribution using the formulation corresponding to any binomial probability distribution; and (d) draw a graph of the probability distribution and comment on its shape.

Expert Solution

orchestra answered 2 years ago

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)

A random variable Y whose distribution is binomial with parameters are n = 500 and p=...

A random variable Y whose distribution is binomial with parameters are n = 500 and p= 0.400, and here Y suggests the number of desired outcomes of the random experiment and n-Y is the number of undesired outcomes obtained from a random experiment of n independent trials. On this random experiment p̂ sample proportion is found as Y/n. (Round your answers to 3 decimal places in all parts.) a)What is the expected value of this statistic? b)Between what limits will...

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...

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 _________.

Identify the parameters p and n in the following binomial distribution scenario. A basketball player has...

Identify the parameters p and n in the following binomial distribution scenario. A basketball player has a 0.511 probability of making a free throw and a 0.489 probability of missing. If the player shoots 25 free throws, we want to know the probability that he makes no more than 10 of them. (Consider made free throws as successes in the binomial distribution.)

The p.d.f of the binomial distribution random variable X with parameters n and p is f(x)...

The p.d.f of the binomial distribution random variable X with parameters n and p is f(x) = n x p x (1 − p) n−x x = 0, 1, 2, ..., n 0 Otherwise Show that a) Pn x=0 f(x) = 1 [10 Marks] b) the MGF of X is given by [(1 − p) + pet ] n . Hence or otherwise show that E[X]=np and var(X)=np(1-p).

Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...

Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p = 0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x; n, p). (Round your answers to four decimal places.) (a) P(15 ≤ X ≤ 20) p P(15 ≤ X ≤ 20) P(14.5 ≤ Normal ≤ 20.5) 0.5 1 2 0.6...

Question