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Normal Distribution What鈥檚 wrong with the following statement? 鈥淏ecause the digits 0, 1, 2, . . . , 9 are the normal results from lottery drawings, such randomly selected numbers have a normal distribution.鈥

Short Answer

Expert verified

The literal meaning of normal is different from the statistical term normal distribution, which signifies a symmetric bell-shaped curve.

Step by step solution

01

Given information

The statement is 鈥淏ecause the digits 0, 1, 2, . . . , 9 are the normal results from lottery drawings, such randomly selected numbers have a normal distribution.鈥

02

Define a normal distribution

A normal distribution is one of the symmetric distributions defined on continuous data and forms a bell-shape, symmetric about the mean measure.

03

Analyze the lottery drawings

Ideally, the drawings from the lottery are expected to be equally likely for each digit. In that case, the probability of drawing each digit is the same, which is 0.1110 in this case as the number of possibilities is10.

The statement with normal results signifies the uniform pick of the digits in a literal sense.

In the case of statistics, a normal distribution is described differently as stated above. Thus, the statement is wrong.

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Most popular questions from this chapter

Standard normal distribution. In Exercise 17-36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, Draw a graph, then find the probability of the given bone density test score. If using technology instead of Table A-2, round answers to four decimal places.

Less than 2.56

Distributions In a continuous uniform distribution,

=minimum+maximum2and=range12

a. Find the mean and standard deviation for the distribution of the waiting times represented in Figure 6-2, which accompanies Exercises 5鈥8.

b. For a continuous uniform distribution with =0and=1, the minimum is-3 and the maximum is 3. For this continuous uniform distribution, find the probability of randomly selecting a value between 鈥1 and 1, and compare it to the value that would be obtained by incorrectly treating the distribution as a standard normal distribution. Does the distribution affect the results very much?

Standard Normal Distribution. Find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Standard Normal DistributionIn Exercises 17鈥36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between 1.50 and 2.50.

Standard Normal DistributionIn Exercises 17鈥36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between -2.00 and 2.00.

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