Explanation Approach: The bell-shaped normal curve is symmetric with respect to its mean (denoted as μ ). Thus, 50% of the data values lies to the left of mean and remaining 50% of the data lies to the right of the mean. Figure 1 illustrates 68-95-99.7 rule for a normal distribution . Figure 1 Approximately 68% of the data lies between μ − σ and μ + σ , 95% of the data lies between μ − 2 σ and μ + 2 σ 99.7% of the data lies between μ − 3 σ and μ + 3 σ . Assume a normal distribution has a mean of μ and a standard deviation of σ . We use the equation z = x − μ σ to convert a value x in the nonstandard distribution to a z -score. Given Information: The mean is 500 and the standard deviation is 100. Calculation: Substitute μ = 500 , σ = 100 and x = 520 in z = x − μ σ , z = 520 − 500 100 = 20 100 = 0.2 Therefore, the corresponding z -score is approximately 0.2. That is, P ( x < 520 ) = P ( z < 0.2 ) . Figure 1 To find the area between z = 0 and to a z -score, use the data in the standard normal distribution table. Use the row for z = 0.7 and the column labelled 0.08 in the standard normal distribution table. The data from the standard normal distribution table required for this problem is given below:

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

See similar textbooks

Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

Videos

Question

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 14.4, Problem 76E

To determine

To find:

The percent of students scoring less than 520 in SAT scores.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 75E

Chapter 14.4, Problem 77E

Students have asked these similar questions

Show that the Laplace equation in Cartesian coordinates: J²u J²u + = 0 მx2 Jy2 can be reduced to the following form in cylindrical polar coordinates: 湯( ди 1 8²u + Or 7,2 მ)2 = 0.

Draw the following graph on the interval πT 5π < x < x≤ 2 2 y = 2 cos(3(x-77)) +3 6+ 5 4- 3 2 1 /2 -π/3 -π/6 Clear All Draw: /6 π/3 π/2 2/3 5/6 x 7/6 4/3 3/2 5/311/6 2 13/67/3 5 Question Help: Video Submit Question Jump to Answer

Determine the moment about the origin O of the force F4i-3j+5k that acts at a Point A. Assume that the position vector of A is (a) r =2i+3j-4k, (b) r=-8i+6j-10k, (c) r=8i-6j+5k

Chapter 14 Solutions

Mathematics All Around (6th Edition)

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The percent of students scoring less than 520 in SAT scores.

Solution Summary: The author illustrates the 68-95-99.7 rule for a normal distribution.

Concept explainers

Videos

To find: The percent of students scoring less than 520 in SAT scores.

Want to see the full answer?

Chapter 14 Solutions

To find:

The percent of students scoring less than 520 in SAT scores.