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.

Short 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.

Step-by-step solution

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,

$n=50$

$STD=16$

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.