Strands of copper wire from a manufacturer are analyzed for strength and conduct
ID: 3201943 • Letter: S
Question
Strands of copper wire from a manufacturer are analyzed for strength and conductivity. The results from 98 strands are as follows: (a) If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high? (b) If a strand is randomly selected, what is the probability that its conductivity is low or the strength is low? (c) Given that a randomly selected strand has low conductivity, what is the probability that it will have low strength? (d) Consider the event that a strand has low conductivity and the event that the strand has a low strength. Are these events mutually exclusive ? (e) Consider the event that a strand has low conductivity and the event that the strand has a low strength. Does the data support the conclusion that these two events are independent? Refer to Question 2. Suppose that we randomly select 5 of the 98 strands of wire, without replacement. (a) What is the probability that all five have high strength ? (b) What is the probability that at most one will have high strength?Explanation / Answer
Result:
n=98
Number of high strength= 89
a).
P (all 5 have high strength)
= (89/98)*(88/97)*(87/96)*(86/95)*(85/94)
=0.611208
b).
P( at most one have high strength)
= P( x=0)+P( x=1)
=(9/98)*(8/97)*(7/96)*(6/95)*(5/94)+5*(89/98)*(9/97)*(8/96)*(7/95)*(6/94)
=0.000166