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 = waiting time between peak hours Find the height of this uniform distribution. 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 = 5 * 0.125 = 0.625 Find the probability of waiting five minutes exactly. P (waiting time exactly five minutes) = 0.000 As this is continuous distribution so at a particular point probability is 0 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%. P (Z z) = 0.15 is z = -1.04 The area to the right of z is 65%. P (Z z) = 0.06500 is z = 0.385 The area to the left of z is 10%. P (Z z) = 0.1 is z = 1.282 The area to the right of z is 5%. P (Z z) = 0.500 is z = 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 is z = 1.96 The area between and z is 99%. P (-z Z z) = 0.99 is z = 2.576 6.3.4 According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed. State the random variable. X = blood pressure for people e in China Find the probability that a person in China has blood pressure of 135 mmHg or more. calculator normalcdf (135,1e99,128,23) = 0.3804 Find the probability that