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1. Consider a binomial experiment with n=30 trials and p=0.40. a. Find the expected value and the standard deviation of the distribution. b. Would it be unusual to obtain fewer than 3 successes? Explain.

1. Consider a binomial experiment with n=30 trials and p=0.40. a. Find the expected value and the standard deviation of the distribution. b. Would it be unusual to obtain fewer than 3 successes? Explain.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 9E
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1. Consider a binomial experiment with n=30 trials and p=0.40. Find the expected value and the standard deviation of the distribution. a. b. Would it be unusual to obtain fewer than 3 successes? Explain. 2. Old Friends Information Service is a California company that is in the business of finding addresses of long- lost friends. Old Friends claims to have a 70% success rate. Suppose that you have the names of six friends for whom you have no addresses and decide to use Old Friends to track them. a. Make a histogram showing the probability of r=0 to 6 friends for whom an address will be found. b. Find the mean c. Find the standard deviation of this probability distribution. d. What is the expected number of friends for whom addresses will be found? 3. Approximately 3.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists. Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit. a. Write out a formula for the probability distribution of the random variable. Find the probabilities that b. n=3 e. Find the probability that n ≥ 5 c. n=5 d. n=12 f. What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use u for the geometric distribution and round.
Transcribed Image Text:1. Consider a binomial experiment with n=30 trials and p=0.40. Find the expected value and the standard deviation of the distribution. a. b. Would it be unusual to obtain fewer than 3 successes? Explain. 2. Old Friends Information Service is a California company that is in the business of finding addresses of long- lost friends. Old Friends claims to have a 70% success rate. Suppose that you have the names of six friends for whom you have no addresses and decide to use Old Friends to track them. a. Make a histogram showing the probability of r=0 to 6 friends for whom an address will be found. b. Find the mean c. Find the standard deviation of this probability distribution. d. What is the expected number of friends for whom addresses will be found? 3. Approximately 3.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists. Let n be a random variable that represents the first Jonathan apple chosen at random that has bitter pit. a. Write out a formula for the probability distribution of the random variable. Find the probabilities that b. n=3 e. Find the probability that n ≥ 5 c. n=5 d. n=12 f. What is the expected number of apples that must be examined to find the first one with bitter pit? Hint: Use u for the geometric distribution and round.
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