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 = 2.02 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.) months² months variance standard deviation (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places)
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 = 2.02 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.) months² months variance standard deviation (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places)
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...
Related questions
Question
![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 \( \mu = 2.02 \) and \( \sigma^2 = 0.03 \) (here the unit for delay is months).
### Exercises
(a) **Variance and Standard Deviation Calculation:**
- **What are the variance and standard deviation of delay time?** (Round your answers to two decimal places.)
- Variance: [________] months\( ^2 \)
- Standard Deviation: [________] months
(b) **Probability of Delay Exceeding a Certain Duration:**
- **What is the probability that delay time exceeds 12 months?** (Round your answer to four decimal places.)
- Probability: [________]
(c) **Probability Within One Standard Deviation:**
- **What is the probability that delay time is within one standard deviation of its mean value?** (Round your answer to four decimal places.)
- Probability: [________]
(d) **Median of the Delay Time Distribution:**
- **What is the median of the delay time distribution?** (Round your answer to two decimal places.)
- Median: [________] months
(e) **99th Percentile of the Delay Time Distribution:**
- **What is the 99th percentile of the delay time distribution?** (Round your answer to two decimal places.)
- 99th Percentile: [________] months
(f) **Expected Number of Items Exceeding a Specific Delay:**
- **Among 10 randomly selected such items, how many would you expect to have a delay time exceeding 6 months?** (Round your answer to three decimal places.)
- Expected Number: [________] items](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F324f16c4-c4e5-4b06-b074-f261b39e021a%2F8c38843c-82f9-4b38-ab60-8c0d5d9237cf%2Fm8mobdb_processed.png&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 \( \mu = 2.02 \) and \( \sigma^2 = 0.03 \) (here the unit for delay is months).
### Exercises
(a) **Variance and Standard Deviation Calculation:**
- **What are the variance and standard deviation of delay time?** (Round your answers to two decimal places.)
- Variance: [________] months\( ^2 \)
- Standard Deviation: [________] months
(b) **Probability of Delay Exceeding a Certain Duration:**
- **What is the probability that delay time exceeds 12 months?** (Round your answer to four decimal places.)
- Probability: [________]
(c) **Probability Within One Standard Deviation:**
- **What is the probability that delay time is within one standard deviation of its mean value?** (Round your answer to four decimal places.)
- Probability: [________]
(d) **Median of the Delay Time Distribution:**
- **What is the median of the delay time distribution?** (Round your answer to two decimal places.)
- Median: [________] months
(e) **99th Percentile of the Delay Time Distribution:**
- **What is the 99th percentile of the delay time distribution?** (Round your answer to two decimal places.)
- 99th Percentile: [________] months
(f) **Expected Number of Items Exceeding a Specific Delay:**
- **Among 10 randomly selected such items, how many would you expect to have a delay time exceeding 6 months?** (Round your answer to three decimal places.)
- Expected Number: [________] items
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 5 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON