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# Histograms, normal distributions, means, variances

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Rent Resident: Amount of monthly profit from residential rent homes

There is a data file attached.

Rent Commercial: Amount of monthly profit from rent paid on commercial buildings.

A realtor owns numerous residential and commercial buildings and collects rent on these properties. The realtor selects 100 months over the past several years and lists the monthly profit in thousands of dollars for these properties. These values are listed in the variables Rent REsident and Rent Commercial, in thousands of dollars.

1. Plot a histogram of the data in rent resident and also of the data in rent commercial. Would you say that the data are approximately normally distributed? Find the mean and variance for each of the variables.

2.What type of distribution do you believe the sum of the rentresident and rentcommercial would have. What do you think the resulting mean and variance would be.

3. Plot a histogram of the sum of the RentResident and RentCommercial. Does the distribution appear to be approximately normally distributed? Find the mean and variance. Compaare these results to your answers in part 2. Is the variance of the sum equal to the sum of the variances?

https://brainmass.com/statistics/descriptive-statistics/histograms-normal-distributions-means-variances-14973

## SOLUTION This solution is FREE courtesy of BrainMass!

1. Histograms of all three distributions are included on the attached Word document. In each case the data are approximately normally distributed. I used Excel to calculate the mean and standard deviation for each of the three distributions and have included them in a table in the Word document. The variances are the squares of the standard deviations.

2. In theory the distribution of the sum should also be normal. See the attached Word document for calculations of the theoretical mean and standard deviation.

3.The histogram of the sum also appears to be approximately normal. The calculated mean is the same as the theoretical mean. The variance of the sum is slightly different than the theoretical variance, which can be explained by sampling error. See the attached word document for details.

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