1. Distribution and Probability

A Highway Patrol Officer is asked to measure how fast cars are travelling down a busy residential road for an entire week. It is thought that the speed limit of this road needs to be changed. The Patrol Officer find the speeds to be normally distributed with a mean of 48mph and a standard deviation of 5mph.

a) Draw the distribution and shade in the area that represents speeds greater than 45mph (Done). What proportion of cars are exceeding the speed limit of 45mph?(Need) Must show work and provide Zscore. (need)

b) Draw the distribution and shade in the are that represents the approximate 10% of car speeds (Done). The top 10% of cars are travelling greater than what speed?(Need)

2. Re: Distribution and Probability

If it is normally distributed, then 50% of drivers are traveling at speeds of 48mph or greater. The cutoff point is 0.6 standard deviations from the mean $\displaystyle \left(48-45 = 3\text{ and }\dfrac{3}{5} = 0.6\right)$. So, use that to find the percent of people driving greater than 45 mph. In other words, find the z-score that is associated to that number of standard deviations from the mean.

For (b), again, this is based on numbers of standard deviations. If you want the top 10%, find how many standard deviations that is equal to, multiply that number by 5, and add it to 48.

3. Re: Distribution and Probability

How would you find the standard deviations it is equal to for B?