The image appears to be a homework assignment involving normal distribution, specifically using z-scores related to IQ scores from a normal distribution. Let’s break down the questions and provide the answers based on the given details.

1) Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) are approximately Normal for the age group of 20 to 34. The mean score is 110 with a standard deviation of 25. What percent of this age group has an IQ below 100?

a) Write the inequality using the raw score:

• The raw score is simply the IQ score, so you would write: $X < 100$ where $X$ represents the IQ score.

b) Find the z-score and rewrite the inequality:

The z-score formula is: $z = \frac{X - \mu}{\sigma}$ where:

• $X = 100$ (the IQ score),
• $\mu = 110$ (mean IQ score),
• $\sigma = 25$ (standard deviation).

Let’s calculate the z-score: $z = \frac{100 - 110}{25} = \frac{-10}{25} = -0.4$

So, the inequality becomes: $z < -0.4$

c) Draw the Normal standardized curve:

For a standard normal curve, the mean is at 0, and values decrease symmetrically to the left and increase to the right. You would mark -0.4 on the x-axis to the left of 0.

d) What are you entering into your calculator?

You would look for the area to the left of $z = -0.4$ in a standard normal distribution table or use a calculator. The value corresponding to $z = -0.4$ is approximately 0.3446, meaning about 34.46% of the population has an IQ below 100.

e) What percent of adults from 20 to 34 have an IQ less than 100?

As calculated, about 34.46% of this age group has an IQ below 100.

Would you like more details or clarification on any part of this problem? Here are some related questions to expand on this topic:

1. How do you calculate the area under a normal distribution curve for values other than $z = -0.4$?
2. What does the area to the right of a z-score represent in a normal distribution?
3. How would the percentage change if the standard deviation were different?
4. Can you find the percentage of people who have an IQ between 90 and 110?
5. What does a z-score of 0 represent in terms of raw data?

Tip: When using a z-score table, ensure you are interpreting the table correctly based on whether you are looking for the left-tail or right-tail probability.