The authors of the paper from which the data in Exercise 1.27 was extracted suggested th...

The authors of the paper from which the data in Exercise 1.27 was extracted suggested that a reasonable probability model for drill lifetime was a lognormal distribution with μ = 4.5 and σ .8.

a. What are the mean value and standard deviation of lifetime?

b. What is the probability that lifetime is at most 100?

c. What is the probability that lifetime is at least 200? Greater than 200?

Referenc exercise 1.27

The paper “Study on the Life Distribution of Microdrills” (J. of Engr. Manufacture, 2002: 301–305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks) when holes were drilled in a certain brass alloy.

a. Why can a frequency distribution not be based on the class intervals 0–50, 50–100, 100–150, and so on?

b. Construct a frequency distribution and histogram of the data using class boundaries 0, 50, 100, . . . , and then comment on interesting characteristics.

c. Construct a frequency distribution and histogram of the natural logarithms of the lifetime observations, and comment on interesting characteristics.

d. What proportion of the lifetime observations in this sample are less than 100? What proportion of the observations are at least 200?