Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 Click to view page 1 of the table. Click to view page 2 of the table. 0.97 The indicated IQ score, x, is (Round to one decimal place as needed.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Transcription and Explanation for Educational Website:**
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### Understanding IQ Scores and Normal Distribution
This exercise involves finding an indicated IQ score using a normal distribution graph.
**Text:**
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and these scores are normally distributed with a mean of 100 and a standard deviation of 15.
- Click to view page 1 of the table. Click to view page 2 of the table.
**Question:**
The indicated IQ score, x, is ______. (Round to one decimal place as needed.)
**Instructions:**
Enter your answer in the answer box.
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**Graph Explanation:**
The graph on the right is a normal distribution curve representing the IQ scores of adults. The curve is centered around a mean of 100, and the spread is determined by a standard deviation of 15. The shaded area under the curve represents the probability or portion of the distribution specified by the problem. For this graph, the shaded area corresponds to 0.97 of the distribution.
To find the specific IQ score, you would typically use a standard normal distribution table or calculator to find the z-score corresponding to the specified probability (0.97), and then use the z-score formula to solve for the IQ score (x):
\[ x = \text{mean} + (\text{z-score} \times \text{standard deviation}) \]
This exercise helps in understanding how to interpret normal distribution graphs and calculate specific data points based on probabilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58efeb35-d412-471f-b0b3-6d1987dd7a8b%2F5d65b333-eeeb-4b32-8b29-3bbe10b42684%2Ffqxxix9_processed.jpeg&w=3840&q=75)
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