76. Let and sn 2 denote the sample mean and variance for the sample x1, . . . , xn and let and s2 n1 denote these quantities when an additional observation xn1 is added to the sample.

a. Show how can be computed from and xn1.

b. Show that so that s2 n1 can be computed from xn1, , and sn 2.

c. Suppose that a sample of 15 strands of drapery yarn has resulted in a sample mean thread elongation of 12.58mmand a sample standard deviation of .512 mm.A16th strand results in an elongation value of 11.8. What are the values of the sample mean and sample standard deviation for all 16 elongation observations?