Sales delay is the elapsed time between the manufacture of a product and its sale. According to the article "Warranty Claims Data Analysis Considering Sales Delay" (Quality and Reliability Engr. Intl., 2013: 113-123), 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 = 2.05 and s2 = .06 (here the unit for delay is months).
a. What are the variance and standard deviation of delay time?
What is the probability that delay time exceeds 12 months?
c. What is the probability that delay time is within one standard deviation of its mean value?
d. What is the median of the delay time distribution?
e. What is the 99th percentile of the delay time distribution?
f. Among 10 randomly selected such items, how many would you expect to have a delay time exceeding 8 months?