Question

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Answer 1

Answer:

0.7233

Step-by-step explanation:

We want to find the area between the z-scores z=-0.95 and z=1.25.

We first find the area to the left of each z-score, and subtract the smaller area from the bigger one.

For the area to the left of z=-0.95, we read -0.9 under 5 from the standard normal distribution table.

This gives P(z<-0.95)=0.1711

Similarly the area to the left of z=1.25 is

P(z<1.25)=0.8944

Now the area between the two z-scores is

P(-0.25<z<1.25)=0.8944-0.1711=0.7233

Answer 2

Using the normal distribution, it is found that the area of the shaded region is of 0.7233.

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Normal Probability Distribution

Z-score formula is used, considering a measure X, mean $\mu$ and standard deviation $\sigma$.

$Z = \frac{X - \mu}{\sigma}$

• Each z-score has an associated p-value, which represents the percentile of the measure X.
• The area between two z-scores is the p-value of the greater z-score subtracted by the p-value of the smaller z-score.

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Looking at the z-table, we get that:

• z = 1.25 has a p-value of 0.8944.
• z = -0.95 has a p-value of 0.1711.

0.8944 - 0.1711 = 0.7233.

The area of the shaded region is of 0.7233.

A similar problem is given at https://brainly.com/question/15404560