You can search for z chart online

New\" 5 The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with a mean of 69 T . \"BS and a standard deviation of 3. (Round your answers to 4 decimal places, if needed.) remaining- 1 Marked out of _ 4.00 [Note: When needed, correct answers use the provided z-table on eclass, but Excel can also be appropriately used] '7 Flag question (a) If a specimen is acceptable only if its hardness is between 63 and 71, what is the probability that a randomly chosen specimen has an acceptable hardness? D (b) If the acceptable range of hardness is (69 c, 69 a cl, for what value of it: would 90% of all specimens have acceptable hardness? [1 (cl If the acceptable ranpe is as in part (a) and the hardness of each of 10 randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the 10'? D (d) What Is the probability that at most 3 of 10 independently selected specimens have a hardness of less than 71.72? B Check W's'i'm 6 A shipping company handles containers in three different sizes: (1) 27 ft3 (3 x 3 x 3), (2) 125 ha, and (3) 512 ft3. Let X,- U = 1, 2, 3) Was remaming: denote the number of type icontainers shipped during a given week. With E(X,-) = u; and VtX = 0,2, suppose that the mean values 1 and standard deviations are as follows. {Round your answers to 4 decimal places, if needed.) Marked out of 2.00 [11 = 330 512 = 300 [.13 = 110 V Flag U1=14 0'2 =13 03 = 9 question [Note: When needed, correct answers use the provided z-table on eClass, but Excel can also be appropriately used.] (a) Assuming that X1. X2, X3 are independent and each follow a normal distribution. what is the probability that the total volume shipped is at most 100,000 ft3? [Hintz See Homework #3, Question 12.] l:] (b) Referring to part (a), what is the probability that the total volume shipped is more than 90,000 ft3'? [:1 Check