Q3. | Recent records show that 40% of candidates become unsuccessful in Whelers Hill rescue training scheme. Suppose that 5 candidates took the test independently under the training scheme. (a) Why would you choose binomial distribution for this problem? (b) Assuming x is the number of successful candidates, construct the probability distribution and draw a bar graph. (c) What is the probability that at least 2 candidates will be successful? (d) What is the probability that exactly 2 candidates will be unsuccessful?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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Q3. Recent records show that 40% of candidates become unsuccessful in Whelers Hill rescue
training scheme. Suppose that 5 candidates took the test independently under the training
scheme.
(a) Why would you choose binomial distribution for this problem?
(b) Assuming x is the number of successful candidates, construct the probability
distribution and draw a bar graph.
(c) What is the probability that at least 2 candidates will be successful?
(d) What is the probability that exactly 2 candidates will be unsuccessful?
Q4. An average of 0.5 robberies occur per day in a large city. Using the Poisson formula, find
the following probabilities.
(a) Exactly 4 robberies will occur in the next week
(b) At least 2 robberies will occur on a given day
Q5. Breckie Electrics makes electric shavers. The life x of an electric shaver manufactured by
this corporation has a normal distribution with a mean of 70 months and a standard deviation
of 10 months. The company is to determine the warranty period for this shaver. Any shaver
that needs a major repair during this warranty period will be replaced free by the company.
(a) What should the warranty period be if the company does not want to replace more than
5% of the shavers?
(b) Find x such that 90% of shavers life is less than x?
(c) What percentage of shavers do not need major servicing before 90 months?
Transcribed Image Text:Q3. Recent records show that 40% of candidates become unsuccessful in Whelers Hill rescue training scheme. Suppose that 5 candidates took the test independently under the training scheme. (a) Why would you choose binomial distribution for this problem? (b) Assuming x is the number of successful candidates, construct the probability distribution and draw a bar graph. (c) What is the probability that at least 2 candidates will be successful? (d) What is the probability that exactly 2 candidates will be unsuccessful? Q4. An average of 0.5 robberies occur per day in a large city. Using the Poisson formula, find the following probabilities. (a) Exactly 4 robberies will occur in the next week (b) At least 2 robberies will occur on a given day Q5. Breckie Electrics makes electric shavers. The life x of an electric shaver manufactured by this corporation has a normal distribution with a mean of 70 months and a standard deviation of 10 months. The company is to determine the warranty period for this shaver. Any shaver that needs a major repair during this warranty period will be replaced free by the company. (a) What should the warranty period be if the company does not want to replace more than 5% of the shavers? (b) Find x such that 90% of shavers life is less than x? (c) What percentage of shavers do not need major servicing before 90 months?
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