a. Explanation Calculation: The given information is that the mean and standard deviation of IQ scores is 100 and 16. The IQ model follows a normal model. Define the random variable Y as the IQ scores. Here, 15 th percentile of the IQ model represents the area of 0.15 to the left of z -score. Software procedure: Step-by-step procedure to obtain z -score by using MINITAB software: Choose Graph > Probability Distribution Plot choose View Probability> OK. From Distribution , choose ‘ Normal ’ distribution. Click the Shaded Area tab. Choose ProbabilityValue and LeftTail for the region of the curve to shade. Enter the Probability as 0.15. Click OK . Output using the MINITAB software is given below: Therefore, the z -value is –1.036. The formula for finding z -score is, z = y − μ σ where μ is the mean and σ is the standard deviation of the variable Y b. To determine Find the IQ that represents the 98 th percentile. c. To determine Find the IQR of the IQs.

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ISBN: 9780321825278

Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock

Publisher: PEARSON

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 5, Problem 46E

To determine

Find the IQ that represents the 15^th percentile.

To determine

Find the IQ that represents the 98^th percentile.

To determine

Find the IQR of the IQs.

Expert Solution & Answer

Chapter 5 Solutions

Intro Stats

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Find the IQ that represents the 15 th percentile.

Concept explainers

Videos

Find the IQ that represents the 15th percentile.

Find the IQ that represents the 98th percentile.

Find the IQR of the IQs.

Chapter 5 Solutions

Find the IQ that represents the 15^th percentile.

Find the IQ that represents the 98^th percentile.