Answered: According to the attached normal…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 1GP

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Question

According to the attached normal distribution graph, which are the z-scores of the graph:

a) -1,96 and 1,96

b) -1,65 and 1,65

c) -1,64 and 1,64

d) -0,07 and 0,07

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.

Expert Solution

Step 1

The normal distribution:

A continuous random variable X is said to follow normal distribution with mean µ and standard deviation σ if the probability density function of X is,

Step 2

It is given that area between 0 and z is 0.475.

It is known that area below (or above) to the point 0 in a standard normal curve is 0.50.

Thus, area between -∞ and lower z is 0.5-0.475 =0.025.

Consider the standard normal table given below:

From the above table lower value of z is -1.96.

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