Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also show that the mean time between arriving patients is $8.7$8 minutes.

a. Use the technology of your choice to simulate four random samples of$75$ interarrival times each.

b. Obtain a normal probability plot of each sample in part (a).

c. Are the normal probability plots in part (b) what you expected? Explain your answer.

To explain simulate the random patients which has $75$interarrival time for each with$8.7$mean time. The number of samples and mean of arrival.

Mean $=8.7$.

Let's take $n=75$

Then sing MATLAB create a random matrix which has the mean $8.7$

We will use the function

$x=F^{-1}(p\mid \mu )$

$=-\mu \ln (1-p)$

Here $\mu$is the mean of arrival time and $p$is the random sample.

$p=$rand$(75,4)$

$\mu =8.7$

Put all the values into the above equation and get the random 4 samples such as

$x=-\ln (1-rand(75,4\left)\right)\times 8.7$

After solving the equation, we will get the answer.

Program:

Query:

We started by determining the quantity of samples.

Then make a matrix with an average arrival time of$8.7$.

We shall arrive at a solution after simplifying.

To determine the create a normal probability plot for the random sample from part (a).

The number of samples and mean of arrival is given.

$n=75$

Mean$=8.7$.

Then sing MATLAB create a random matrix which has the mean $8.7$

We will use the function

$x=F^{-1}(p\mid \mu )$

$=-\mu \ln (1-p)$

Here $\mu$is the mean of arrival time and $p$is the random sample.

$p=rand(75,4)$

$\mu =8.7$

Put all the values into the above equation and get the random $4$samples such as

$x=-\ln (1-rand(75,4\left)\right)\times 8.7$

After solving the equation, we will get the answer.

Program:

Query:

We began by calculating the number of samples required.

Make a matrix with an $8.7$average arrival time.

After simplifying, we'll arrive at a solution.

Draw a graph of the samples' normal probability distribution.

Explain your answer what would you expect from normal probability plot from part (b).

The figure the population distribution is normally distributed.

If the probability plot is regular linear, the variables are roughly normally distributed; if the plot is not regular linear, the variables are not roughly normally distributed.