Question

1. The breaking strengths (measured in dynes) of nylon fibers are normally distributed with a
mean of 12,500 and a variance of 202,500.
a) What is the probability that a fiber strength is more than 13,175?
b) What is the probability that a fiber strength is less than 11,600?
c) What is the probability that a fiber strength is between 12,284 and 15,200?
d) What is the 90 th percentile of the fiber breaking strength?

2.

1. Suppose that X, Y and Z are independent random variables such that X~N1, 4 (i.e. X is normally distributed with mean 1 and variance 4), Y~N-3, 9   and Z~N-2, 6.

1. Find the probability that X-Y≤3-X

2. Find the value of c such that probability that P 2X+3Y-2Z+3≥c=.8384

3. If you draw a random sample of size n = 16 from the distribution of the random variable X described above, what is probability that the absolute value of the sample mean will be less than 1.25?

3.

You are given two independent random variables, one that is and the second random variable
named Y , is ; both and are unknown parameters . You wish to estimate . You draw two independent
samples each of size 16 one from the Bernouilli population and the other sample from the population of Y.
Let X be the number of successes from the Bernouilli sample and let be the sample mean from the normal
sample. Consider to be a point estimator of .
a) Is an unbiased point estimator of ? Justify your answer.
b) Find another estimator of that is unbiased?
c) If , for what value(s) of , the mean square error of is smaller than the mean square error
of found in part b)?

Answer 1