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Chapter 6: Q2 (page 250)

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?

Short Answer

Expert verified

a. The area under the curve is equal to 1.

b. The median is equal to 3152.0 grams.

c. The mode is equal to 3152.0 grams.

d. The variance is equal to 480803.6 grams.

Step by step solution

01

Given information

The birth weights are normally distributed with a mean equal to 3152.0 grams and a standard deviation equal to 693.4 grams.

02

Normal distribution

Normal distribution has the following properties:

  • The data that follows a normal distribution has a bell-shaped graph, and the area under the curve is equal to 1.
  • The mean, median, and modal values for a given normal distribution are all equal.

a.

The area under the graph is equal to 1.

b.

The median value is equal to 3152.0 grams.

c.

The mode value is equal to 3152.0 grams.

d.

The variance is computed as follows:

Variance=standarddeviation2=693.42=480803.6grams

Thus, the variance is equal to 480803.6 grams.

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