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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 = 2.01 and ² = 0.07 (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.) months² months variance 2.72 standard deviation 1.65 x X (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) 0.0217 X (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.) 0.6942 X

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 = 2.01 and ² = 0.07 (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.) months² months variance 2.72 standard deviation 1.65 x X (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) 0.0217 X (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.) 0.6942 X

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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**Sales Delay and Lognormal Distribution Analysis** Sales delay is the elapsed time between the manufacture of a product and its sale. It is quite common to model sales delay using a lognormal distribution. For a specific product, this distribution is characterized by parameter values \( \mu = 2.01 \) and \( \sigma^2 = 0.07 \) (the unit for delay is months). ### Calculations: **(a) Variance and Standard Deviation of Delay Time:** - **Variance:** 2.72 months\(^2\) - **Standard Deviation:** 1.65 months **(b) Probability of Delay Time Exceeds 12 Months:** - Probability: 0.0217 **(c) Probability that Delay Time is Within One Standard Deviation of Its Mean:** - Probability: 0.6942 **(d) Median of the Delay Time Distribution:** - Median: 8.00 months **(e) 99th Percentile of the Delay Time Distribution:** - 99th Percentile: 12.75 months **(f) Expected Number of Items with Delay Time Exceeding 9 Months (out of 10 Randomly Selected Items):** - Expected Number: 0.001 items *Note: The red crosses indicate that the provided answers in the fields may be incorrect, suggesting a need to review calculations or inputs.*
Transcribed Image Text:**Sales Delay and Lognormal Distribution Analysis** Sales delay is the elapsed time between the manufacture of a product and its sale. It is quite common to model sales delay using a lognormal distribution. For a specific product, this distribution is characterized by parameter values \( \mu = 2.01 \) and \( \sigma^2 = 0.07 \) (the unit for delay is months). ### Calculations: **(a) Variance and Standard Deviation of Delay Time:** - **Variance:** 2.72 months\(^2\) - **Standard Deviation:** 1.65 months **(b) Probability of Delay Time Exceeds 12 Months:** - Probability: 0.0217 **(c) Probability that Delay Time is Within One Standard Deviation of Its Mean:** - Probability: 0.6942 **(d) Median of the Delay Time Distribution:** - Median: 8.00 months **(e) 99th Percentile of the Delay Time Distribution:** - 99th Percentile: 12.75 months **(f) Expected Number of Items with Delay Time Exceeding 9 Months (out of 10 Randomly Selected Items):** - Expected Number: 0.001 items *Note: The red crosses indicate that the provided answers in the fields may be incorrect, suggesting a need to review calculations or inputs.*
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