Asked Jan 16, 2020

Birth Weights Based on Data Set 4 “Births” in Appendix B, birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g.

a. For the bell-shaped graph, what is the area under the curve?

b. What is the value of the median?

c. What is the value of the mode?

d. What is the value of the variance?


Expert Answer

Step 1

a. Area under the curve for a bell-shaped graph:

The birth weights follow a normal distribution with a mean of 3,152.0 g and a standard deviation of 693.4 g.

Here, the normal distribution of the bell-shaped graph and its area is equal to 1. That is, the total area under the curve is 1.

Step 2

b. Value of the median:

The random variable x represents the birth weights.

For the normal distribution, the mean is equal to the median.

Thus, the value of the median is 3,152 g.

Step 3

c. Value of the mode:

For the normal distribution, the mean is equal to the mode.


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