STAT 200 Week 4 Homework Problems Solutions, University of Maryland University College (UMUC)

STAT 200 Week 4 Homework Problems 6.1.2 1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH, have a waiting time during peak rush hour periods of eight minutes ("2012 annual report," 2012). a.) State the random variable. x=waiting time during peak hours b.) Find the height of this uniform distribution. 1/(8-0)=0.125 c.) Find the probability of waiting between four and five minutes. P(4<x<5)=(5-4)*0.125=0.125 d.) Find the probability of waiting between three and eight minutes. P(3<x<8)=(8-3)*0.125=0.625 e.) Find the probability of waiting five minutes exactly. P(x=5)=0*0.125=0.000 6.3.2 Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean of and standard deviation . a.) The area to the left of z is 15%. Computation in google sheets =NORMINV(0.15,0,1)= -1.036 b.) The area to the right of z is 65%. Computation in google sheets =NORMINV (0.35,0,1)= -0.385 c.) The area to the left of z is 10%. Computation in google sheets =NORMINV(0.1,0,1)= -1.282 d.) The area to the right of z is 5%. Computation in google sheets =NORMINV(0.95,0,1)= 1.645 e.) The area between and z is 95%. (Hint draw a picture and figure out the area to the left of the .) Computation in google sheets =NORMSINV(0.95)= -1.645;1.645 f.) The area between and z is 99%. Computation in google sheets =NORMSINV(0.99)=-2.326;2.326