Business and economics?

Question

1)The fares received by taxi drivers working for the city Taxi line are normally distributed with a mean of $12.50 and a standard deviation equal to $3.25. Based on this information, what is the probability that a specific fare will exceed $15.00?

2) The money spent by people at an amusement park, after paying to get into the gate, is thought to be uniformly distributed between $5.00 and $25.00. What is the probability that they will spend between $8.00 and $15.00?

Answer 1

These are normal distribution questions.

(1) (15.00-12.5)/3.25= 0.7692 which is the z-score.
Look this up in a z-score table for standard distribution and you get 22.0887% (make sure you're looking at right-hand side results of the curve. otherwise, substract the result from 100%).

(2)If money spent is evenly distributed, then the mean is (5+25)/2 = 15
Yo have 2 observations, so you calculate sd using these:
Square root(sum of squared deviations / N)
so, square root (125/2)

sd=7.9057 roughly 8

z-score= (8-15)/8=-0.8750

This gives you a result of 19.0787%, but that is the probability you get less than $8.00. Since you're looking at the lower end of the bell curve ('cause of the negative sign), you need to subtract that result from 50%, and you get 30.92% chance of between $8.00 and $15.00