Consider a small shop with only one checkout counter. The arrivals of customers are distributed throughout the day such that a line rarely forms at the counter. Suppose the arrival times of customers at the counter follows the Exponential Distribution: X ~ Еap(0.4). 0.4 0.3 0.2 0.1 0.0 0.0 2.5 5.0 7.5 10.0 12.5 15.0 a. What is the mean time (in minutes) between customers? b. Determine the following probability. P(2 < X < 10) = (x)

May is tornado season in Oklahoma. According to the National Weather Service, the Poisson rate of tornados in Oklahoma in May is 0.7 per day, based on data from 1950 to the present. The meteorologist is interested in X= the time (in days) from the start of May until the 3rd tornado to occur. Which distribution is an appropriate model for the distribution of X? Gamma Poisson Exponential Beta

Terri Vogel, an amateur motorcycle racer, averages 129.14 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.28 seconds . The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible.b. Find the proportion of her laps that are completed between 131.08 and 134.03 seconds. ___________________c. The fastest 2% of laps are under  seconds.____________________d. The middle 70% of her laps are from ____ seconds to  ____ seconds.

Complete the following table From the frequency distribution, find the mean.  Interval Midpoint x Frequency F Product xf 41.5-48.5   11   48.5-55.5   15   55.5-62.5   19   62.5-69.5   25   69.5-76.5   3   76.5-83.5   2