Question

In: Statistics and Probability

1. (Use Computer) Let X represent a binomial random variable with n = 400 and p...

1.

(Use Computer) Let X represent a binomial random variable with n = 400 and p = 0.8. Find the following probabilities. (Round your final answers to 4 decimal places.)

	Probability
a. P(X ≤ 330)
b. P(X > 340)
c. P(335 ≤ X ≤ 345)
d. P(X = 300)

2.

(Use computer) Suppose 38% of recent college graduates plan on pursuing a graduate degree. Twenty three recent college graduates are randomly selected.

a.	What is the probability that no more than five of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)

b.	What is the probability that exactly nine of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)

c.	What is the probability that at least nine but no more than twelve of the college graduates plan to pursue a graduate degree? (Round your final answer to 4 decimal places.)

3.

Let the mean success rate of a Poisson process be 7 successes per hour.

a.	Find the expected number of successes in a 27 minutes period. (Round your final answer to 1 decimal place.)

b.	Find the probability of at least 2 successes in a given 27 minutes period. (Round your answer to 4 decimal places.)

c.	Find the expected number of successes in a two hours 6 minutes period. (Round your final answer to 1 decimal place.)

d.	Find the probability of 14 successes in a given two hours 6 minutes period. (Round your answer to 4 decimal places.)

4.

(Use computer) Assume that X is a Poisson random variable with μ = 28. Calculate the following probabilities. (Round your final answers to 4 decimal places.)


a. P(X ≤ 18)
b. P(X = 20)
c. P(X > 22)
d. P(24 ≤ X ≤ 32)

Expert Solution

orchestra answered 1 year ago

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