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Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n = 40 trials and probability of success p = 0.85. (a) Is it appropriate to use a normal approximation to this binomial distribu- tion? Why? (b) Compute μ and or of the approximating normal distribution. (c) Use a continuity correction factor to convert the statement r < 30 suc- cesses to a statement about the corresponding normal variable x. (d) Estimate P(r< 30). (e) Interpretation Is it unusual for a binomial experiment with 40 trials and probability of success 0.85 to have fewer than 30 successes? Explain.

Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n = 40 trials and probability of success p = 0.85. (a) Is it appropriate to use a normal approximation to this binomial distribu- tion? Why? (b) Compute μ and or of the approximating normal distribution. (c) Use a continuity correction factor to convert the statement r < 30 suc- cesses to a statement about the corresponding normal variable x. (d) Estimate P(r< 30). (e) Interpretation Is it unusual for a binomial experiment with 40 trials and probability of success 0.85 to have fewer than 30 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.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 54E
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4. Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n = 40 trials and probability of success p = 0.85. (a) Is it appropriate to use a normal approximation to this binomial distribu- tion? Why? (b) Compute u and or of the approximating normal distribution. (c) Use a continuity correction factor to convert the statement r < 30 suc- cesses to a statement about the corresponding normal variable x. (d) Estimate P(r< 30). (e) Interpretation Is it unusual for a binomial experiment with 40 trials and probability of success 0.85 to have fewer than 30 successes? Explain. 5. Critical Thinking You need to compute the probability of 5 or fewer suc- cesses for a binomial experiment with 10 trials. The probability of success on a single trial is 0.43. Since this probability of success is not in the table, you decide to use the normal approximation to the binomial. Is this an appropriate strategy? Explain. 6. Critical Thinking Consider a binomial experiment with 20 trials and proba- bility 0.45 of success on a single trial. (a) Use the binomial distribution to find the probability of exactly 10 suc- cesses. (b) Use the normal distribution to approximate the probability of exactly 10 successes. (c) Compare the results of parts (a) and (b).
Transcribed Image Text:4. Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n = 40 trials and probability of success p = 0.85. (a) Is it appropriate to use a normal approximation to this binomial distribu- tion? Why? (b) Compute u and or of the approximating normal distribution. (c) Use a continuity correction factor to convert the statement r < 30 suc- cesses to a statement about the corresponding normal variable x. (d) Estimate P(r< 30). (e) Interpretation Is it unusual for a binomial experiment with 40 trials and probability of success 0.85 to have fewer than 30 successes? Explain. 5. Critical Thinking You need to compute the probability of 5 or fewer suc- cesses for a binomial experiment with 10 trials. The probability of success on a single trial is 0.43. Since this probability of success is not in the table, you decide to use the normal approximation to the binomial. Is this an appropriate strategy? Explain. 6. Critical Thinking Consider a binomial experiment with 20 trials and proba- bility 0.45 of success on a single trial. (a) Use the binomial distribution to find the probability of exactly 10 suc- cesses. (b) Use the normal distribution to approximate the probability of exactly 10 successes. (c) Compare the results of parts (a) and (b).
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