Assume The Speed Of Vehicles Along A Stretch Of I-10

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?P(X<=65) = P(Z<= (65-71)/8) = P(Z<=-0.75) = 0.2266b. What proportion of the vehicles would be going less than 50 mph?P(X<50) = P(Z< (50-71)/8) = P(Z<-2.625) = 0.0043c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?P(X>x) = 0.1P(Z> (x-71)/8) = 0.1(x-71)/8 = 1.28x = 81.24The new speed limit is 81.24 mphd. In what way do you think the actual distribution of speeds differs from a normal distribution?As people tends to over-speed, the actual distribution should be negatively skewed.A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4. (a) Everyone who scores in the top 30% of the distribution gets a certificate. What is the lowest score someone can get and still earn a certificate? (b) The