a softball player named Jen. You were asked to find the probability of Jen getting at...
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a softball player named Jen. You were asked to find the probability of Jen getting at least 12 hits in her next 20 at bats when she has a batting average of 0.400. Because we have the technology to find binomial probabilities (and their sums) quickly we could have said P(x > 12) = 1- P(x < 11) = 1-0.9435=0.0565 where we find P(x <11) = 0.9435 by using the graphing calculator function binomcdf(20, 0.4, 11) or potentially some other form of technology. a) Suppose we didn't have access to technology that would have found the 0.0565 answer quickly. Use the Normal Distribution as an approximation for the Binomial Distribution. Find the mean and standard deviation of the binomial distribution where X~B(20, 0.4) Mean = Standard Deviation = b) Using the mean and standard deviation from part a in a Normal Distribution, find the z-score that would equate to 12. Round your z-score to two decimal places Z= c) Using the z-score from part b and either the Normal Table or a normalcdf function, find the P(x> 12) in a normal distribution. Round your answer to four decimal places. Comment on how your answer using normal approximation compares to the exact value of 0.0565. P(x > 12) = d) Sometimes the difference between discrete distributions (like binomial) and continuous distributions (like normal) cause these approximations to be off by more than necessary. In this problem, getting 12 hits is really like getting over 11.5 hits if we thought of hits on a continuous scale. Find the z-score that would equate to 11.5 and then using that z-score and either the Normal Table or a normalcdf function, find the P(x > 11.5) in a normal distribution. Round your 2-score to two decimal places and probability to four decimal places. Comment on how your answer using normal approximation compares to the exact value of 0.0565 and also how it compares to your answer in part c. P(x>11.5) = P(Z >_________ a softball player named Jen. You were asked to find the probability of Jen getting at least 12 hits in her next 20 at bats when she has a batting average of 0.400. Because we have the technology to find binomial probabilities (and their sums) quickly we could have said P(x > 12) = 1- P(x < 11) = 1-0.9435=0.0565 where we find P(x <11) = 0.9435 by using the graphing calculator function binomcdf(20, 0.4, 11) or potentially some other form of technology. a) Suppose we didn't have access to technology that would have found the 0.0565 answer quickly. Use the Normal Distribution as an approximation for the Binomial Distribution. Find the mean and standard deviation of the binomial distribution where X~B(20, 0.4) Mean = Standard Deviation = b) Using the mean and standard deviation from part a in a Normal Distribution, find the z-score that would equate to 12. Round your z-score to two decimal places Z= c) Using the z-score from part b and either the Normal Table or a normalcdf function, find the P(x> 12) in a normal distribution. Round your answer to four decimal places. Comment on how your answer using normal approximation compares to the exact value of 0.0565. P(x > 12) = d) Sometimes the difference between discrete distributions (like binomial) and continuous distributions (like normal) cause these approximations to be off by more than necessary. In this problem, getting 12 hits is really like getting over 11.5 hits if we thought of hits on a continuous scale. Find the z-score that would equate to 11.5 and then using that z-score and either the Normal Table or a normalcdf function, find the P(x > 11.5) in a normal distribution. Round your 2-score to two decimal places and probability to four decimal places. Comment on how your answer using normal approximation compares to the exact value of 0.0565 and also how it compares to your answer in part c. P(x>11.5) = P(Z >_________
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Related Book For
Quantitative Methods for Business
ISBN: 978-0840062345
12th edition
Authors: David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey Cam
Posted Date:
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