Question

1. Suppose the number of cracks along a 100 km pipeline follows a normal distribution with Il = 25 and o = 5: • What is the probability that the number of cracks will be at least 30? Will exceed 30 min? (2+1=3 pts) What value c is such that the interval (25 - 0,25 + c) includes 98% of all cracks?! (1+2-3 pts) [Hint: Draw a standard normal curve, think about the meaning of area under the curve, the corresponding z values for c etc.] 2. Suppose the scholarship (S) of a randomly selected recipient is normally distributed with mean u = $2,750 and standard deviation o = $750. a. If a random sample of 25 recipient is selected, what is the probability that the sample average scholarship is at most $2,950? Which Z score did you choose from the Standard Normal table? (2 pts) b. How large a sample size would be required to ensure that the probability in part (a) is at least.99? (3pts)

Answer 1

Problem 1 X has a normal distribution with u = 25, 0 =5 a) P(x > 30) =1- P(*< 30525) 5 =1-P(z<1.00) =1-0.8413 (using z value table) =0.1587 b) P(25-c<x<25+c)= 0.98 P(25-5-25 < ***< 25+6=25) =0.98 P(-c/5<z<c/5)=0.98 2P(z< c/5)-1 =0.98 P(z<c/5)=(1+0.98)/2 P(z<c/5) =0.99 c/5 = 2.33 (using z value table) c=2.33*5 = 11.65

P(25-c<x45+c) =98% 10 is 20 25 X=25-c 30 x=25+c