STAT 200 Week 4 Homework Problems

STAT 200 Week 4 Homework Problems 6.1.2 ⦁ 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). ⦁ State the random variable. X=The waiting time of the trains on the Red Line ⦁ Find the height of this uniform distribution. F(x)= 1/8-0 = 0.125 ⦁ Find the probability of waiting between four and five minutes. P(4<X<5)= (5-4)*0.125 = 0.125 ⦁ Find the probability of waiting between three and eight minutes. P(3<X<8)= (8-3)*0.125= 0.625 ⦁ Find the probability of waiting five minutes exactly. Probability of waiting 5 minutes exactly is 0 since continuous distribution at a particular point is zero. 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 . ⦁ The area to the left of z is 15%. -1.04+(-1.03+1.04)*(8/23)=-1.0365 ⦁ The area to the right of z is 65%. -0.39+(-0.38+0.39)*(17/37)=-0.3854 ⦁ The area to the left of z is 10%. -1.29+(-1.28+1.29)*(5/6)=-1.2817 ⦁ The area to the right of z is 5%. 1.65+(1.64-1.65)*(1/2)=1.645 ⦁ The area between and z is 95%. (Hint draw a picture and figure out the area to the left of the .) P(-z<Z<z)=0.95 ⦁ The area between and z is 99%. P(-z<Z<z)=0.99 -2.58+(-2.57+2.58)*(1/2)=-2.575