Q. 6.139 - Elementary Statistics

Question

Gestation Periods of Humans. mean of 266 days and a standard deviation of 16 days.

a. Use the technology of your choice to simulate four random samples of 50 human gestation periods 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.

Step-by-Step Solution

Answer

a.  The solution is random samples of $50$human gestation periods each.

b. The normal probability plot will be 

c. As we can see in the figure the population distribution is normally distributed.

Part (a) Step 1: Given Information

Simulate the random human gestation period using technology of your choice.

Part (a) Step 2: Explanation

The number of samples, standard deviation and mean is given,

$n=50$

$S T D=16$

Mean$=266$

Let's take $n=50$

Then, in MATLAB, generate a random matrix with a standard deviation of and a mean of.

To make a matrix, we'll utilize  the "norminv" function.

We'll use the function "rand" $(50,1)$ to generate a random sample.

Part (a) Step 3: Explanation

Program:

Query: 

We started by determining the quantity of samples.

Then, using the "norminv" function, make a matrix with a standard deviation of $16$and a mean of $266$.

Part (b) Step 1: Given Information

Create a normal probability plot for the random sample from part (a).

Part (b) Step 2: Explanation

Let's take $n=50$

Create a random matrix in MATLAB with a standard deviation of $16$ and a mean of $266$

To make a matrix, we'll utilize the "norminv" function.

We'll use the function "rand $(50,1)$" to generate a random sample.

Then, using the function "normplot," make a normal probability plot.

Part (b) Step 3: Explanation

Program,

Query: 

We started by determining the quantity of samples.

Then, with the help of the "norminv" function, generate a matrix with a standard deviation of $16$ and a mean of $266$.

Then, using the function "normplot," draw a graph for normal probability.

Part (c) Step 1: Given Information

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

Part (c) Step 2: Explanation

If the probability plot is regular linear, the variables are approximately normally distributed.

The variables are not approximately normally distributed if the plot is not regular linear.