
Section 2.2: Probability
2.21. Consider Figure 2.8 where d
av
= 50 mm and 50 shafts are manufactured. From the measurements
we observe that
25 have the diameter d
av
10 have the diameter 1.01 d
av
6 have the diameter 1.02 d
av
5 have the diameter 0.99 d
av
4 have the diameter 0.98 d
av
.
Sketch the frequency diagram showing appropriate numbers along the axes. Using the frequency inter-
pretation for probability, calculate the probability of occurrence for each shaft size and verify that the
sum of these probabilities equals 1.
Solution: We are given that d
av
= 50 mm and the number of shafts manufactured is 50. Also, the following
measurements are observed:
25 ha ...