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Sales delay is the elapsed time between the manufacture of a product and its sale. According an article it is quite common for investigators to model sales delay using a lognormal distribution. For a particular product, the cited article proposes this distribution with parameter values μ = 2.08 and 2 = 0.03 (here the unit for delay is months). USE SALT (a) What are the variance and standard deviation of delay time? (Round your answers to two decimal places.) variance 2.01 months² standard deviation 1.42 ✔ months (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) 0096 (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.) 0.8485 x (d) What is the median of the delay time distribution? (Round your answer to two decimal places.) 8.00 ✔ months (e) What is the 99th percentile of the delay time distribution? (Round your answer to two decimal places.) months (f) Among 10 randomly selected such items, how many would you expect to have a delay time exceeding 8 months? (Round your answer to three decimal places.) items

Sales delay is the elapsed time between the manufacture of a product and its sale. According an article it is quite common for investigators to model sales delay using a lognormal distribution. For a particular product, the cited article proposes this distribution with parameter values μ = 2.08 and 2 = 0.03 (here the unit for delay is months). USE SALT (a) What are the variance and standard deviation of delay time? (Round your answers to two decimal places.) variance 2.01 months² standard deviation 1.42 ✔ months (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) 0096 (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.) 0.8485 x (d) What is the median of the delay time distribution? (Round your answer to two decimal places.) 8.00 ✔ months (e) What is the 99th percentile of the delay time distribution? (Round your answer to two decimal places.) months (f) Among 10 randomly selected such items, how many would you expect to have a delay time exceeding 8 months? (Round your answer to three decimal places.) items

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Sales delay is the elapsed time between the manufacture of a product and its sale. According to an article, it is quite common for investigators to model sales delay using a lognormal distribution. For a particular product, the cited article proposes this distribution with parameter values \( \mu = 2.08 \) and \( \sigma^2 = 0.03 \) (here the unit for delay is months). ### (a) Variance and Standard Deviation of Delay Time - **Variance**: \(2.01 \, \text{months}^2\) ✓ - **Standard Deviation**: \(1.42 \, \text{months}\) ✓ ### (b) Probability that Delay Time Exceeds 12 Months - \(0.0096\) ✓ ### (c) Probability that Delay Time is Within One Standard Deviation of its Mean Value - \(0.8485\) ✗ ### (d) Median of the Delay Time Distribution - \(8.00 \, \text{months}\) ### (e) 99th Percentile of the Delay Time Distribution - **Months**: (Answer rounded to two decimal places is not provided in the image) ### (f) Expectation of Delay Time Exceeding 8 Months Among 10 Randomly Selected Items - \(7.430 \, \text{items}\) Note: You may need to use the appropriate table in the Appendix of Tables to answer these questions.
Transcribed Image Text:Sales delay is the elapsed time between the manufacture of a product and its sale. According to an article, it is quite common for investigators to model sales delay using a lognormal distribution. For a particular product, the cited article proposes this distribution with parameter values \( \mu = 2.08 \) and \( \sigma^2 = 0.03 \) (here the unit for delay is months). ### (a) Variance and Standard Deviation of Delay Time - **Variance**: \(2.01 \, \text{months}^2\) ✓ - **Standard Deviation**: \(1.42 \, \text{months}\) ✓ ### (b) Probability that Delay Time Exceeds 12 Months - \(0.0096\) ✓ ### (c) Probability that Delay Time is Within One Standard Deviation of its Mean Value - \(0.8485\) ✗ ### (d) Median of the Delay Time Distribution - \(8.00 \, \text{months}\) ### (e) 99th Percentile of the Delay Time Distribution - **Months**: (Answer rounded to two decimal places is not provided in the image) ### (f) Expectation of Delay Time Exceeding 8 Months Among 10 Randomly Selected Items - \(7.430 \, \text{items}\) Note: You may need to use the appropriate table in the Appendix of Tables to answer these questions.
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