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. particular product, the cited article proposes this distribution with parameter values u = 2.08 and a? = 0.04 (here the unit for delay is months).
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. particular product, the cited article proposes this distribution with parameter values u = 2.08 and a? = 0.04 (here the unit for delay is months).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Please help me answer questions c,d,e, and f
![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 \( \sigma^2 = 0.04 \) (here the unit for delay is months).
**Questions and Solutions:**
(a) What are the variance and standard deviation of delay time? (Round your answers to two decimal places.)
- Variance: \( 2.72 \) months\(^2\)
- Standard deviation: \( 1.65 \) months
(b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.)
- Probability: \( 0.0217 \)
(c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.)
- Probability: [Blank space for answer]
(d) What is the median of the delay time distribution? (Round your answer to two decimal places.)
- Median: [Blank space for answer] months
(e) What is the 99th percentile of the delay time distribution? (Round your answer to two decimal places.)
- 99th percentile: [Blank space for answer] months
(f) Among 10 randomly selected such items, how many would you expect to have a delay time exceeding 7 months? (Round your answer to three decimal places.)
- Expected items: [Blank space for answer]
This set of questions involves the application of statistical methods to model the delay time using a lognormal distribution. The variance and standard deviation have been given, along with the probability that delay time exceeds a certain threshold. The activity requires further calculations to complete all answers, which can enhance understanding of probability distributions in practical scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf2a9245-87db-4e54-b147-768ccba693e7%2F2c82bf22-1550-47c7-b4e0-36cca5fc0539%2Fmbhb7sl_processed.jpeg&w=3840&q=75)
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 \( \sigma^2 = 0.04 \) (here the unit for delay is months).
**Questions and Solutions:**
(a) What are the variance and standard deviation of delay time? (Round your answers to two decimal places.)
- Variance: \( 2.72 \) months\(^2\)
- Standard deviation: \( 1.65 \) months
(b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.)
- Probability: \( 0.0217 \)
(c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.)
- Probability: [Blank space for answer]
(d) What is the median of the delay time distribution? (Round your answer to two decimal places.)
- Median: [Blank space for answer] months
(e) What is the 99th percentile of the delay time distribution? (Round your answer to two decimal places.)
- 99th percentile: [Blank space for answer] months
(f) Among 10 randomly selected such items, how many would you expect to have a delay time exceeding 7 months? (Round your answer to three decimal places.)
- Expected items: [Blank space for answer]
This set of questions involves the application of statistical methods to model the delay time using a lognormal distribution. The variance and standard deviation have been given, along with the probability that delay time exceeds a certain threshold. The activity requires further calculations to complete all answers, which can enhance understanding of probability distributions in practical scenarios.
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