Applications of Normal Distributions

Applications of

In this section we work with nonstandard normal distributions (the kind that are found in nature).To work with nonstandard normal distributions we simply standardize them, and use the techniques from the previous section.orWe use our calculators!

Applications of

In this section we work with nonstandard normal distributions (the kind that are found in nature).To work with nonstandard normal distributions we simply standardize them, and use the techniques from 6-2.

Applications of

Converting from a nonstandard to a standard normal distribution.1. Sketch a normal curve, label the mean and the specific x values, then shade the region representing the desired probability.2. For each relevant value x that is a boundary for the shaded region , find the equivalent z-score.3. Use a calculator (normcdf(lower, upper)) or table to find the area in the shaded region.

Applications of

The typical home doorway has a height of 6 ft 8 in. or 80 in. Given that heights of men are normally distributed with a mean of 69.0 in. And a standard deviation of 2.8. Find the percentage of men who can fit through a standard doorway without having to duck.

Applications of

Birth weights in the U.S. are normally distributed with a mean of 3420 g and a standard deviation of 495 g. A hospital requires a special treatment for babies that are less than 2450 g or more than 4390 g. What is the percentage of babies who do not require special treatment. Do many babies require special treatment.

Applications of

Finding Values from Known Areas1. Sketch a normal distribution curve, enter the given probability or percentage in the appropriate region of the graph, and identify the x value(s)2. Use table or calculator invNorm(area to left, mean, stdev) to find the corresponding z-score.3. Convert z-score to x-value 4. Refer to you sketch of the normal curve to verify that the solution makes sense in the context of the graph and in the context of the problem

Applications of

How high should doorways be if 95% of men will fit through without bending or bumping their head? Heights of men are normally distributed with a mean of 69.0 in. and a standard deviation of 2.8 in.

Applications of

After considering relevant factors, a committee recommends special treatment for birth weights in the lowest 3% and the highest 1%. Find the birth weights that separate the lowest 3% and the highest 1%. Recall birth weights in the U.S. are normally distributed with a mean of 3420 g and a standard deviation of 495 g.

Homework!!!

• 6.2: 1- 41 eoo