**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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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 41 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.2 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level? Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part 1) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value Part 2) Alpha (Enter an exact number as an integer, fraction, or decimal.)α = Part 3) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper…
Data can be approximated quite well by a N(3.4, 3.1) model. Economists become alarmed when productivity decreases. According to the normal model what is the probability that the percent change in worker output per hour from the previous quarter is more than 1.6 standard deviations below the mean? What is the probability that the percent change in worker output from the previous quarter is between -1.56 and 4.33?
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Growth of bacteria culture after one week, represented by its size, is known to follow lognormal distribution with mean of 2 and variance of 0.2. What is the upper and lower quartile of the size of the culture after one week?
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