1. A total of 58 AISI 1018 cold-drawn steel bars were tested to determine the 0.2 percent offset yield strength Sy . The results were   where Sy is the class midpoint and f is the class frequency....

1. A total of 58 AISI 1018 cold-drawn steel bars were tested to determine the 0.2 percent offset yield strength
Sy
. The results were

where
Sy
is the class midpoint and
f
is the class frequency. Estimate the mean and standard

deviation of
Sy
and its PDF assuming a normal distribution. 2. The base 10 logarithm of 55 cycles-to-failure observations on specimens subjected to a constant stress level in fatigue have been classified as follows:

Here
y
is the class midpoint and
f
is the class frequency.

(a) Estimate the mean and standard deviation of the population from which the sample was taken

and establish the normal PDF.

(b) Plot the histogram and superpose the predicted class frequency from the normal fit.