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Chapter 6: Q6.18 (page 261)

Which normal distribution has a wider spread, the one with mean 1 and standard deviation 2 or the one with mean 2 and standard deviation 1. Answer true or false to each statement & explain your answers

a. The two normal distributions have same spread

b. The two normal distributions are centred at the same place.

Short Answer

Expert verified

Distribution with mean 1 and standard deviation 2 has wider spread.

A) is False ; B) is False

Step by step solution

01

'Spread' Basics

Spread is a measure of variability of data around the mean, it indicates on average that how far (or distant or varying or different) are the other data points from mean, or how much scattered they are around mean.

02

Standard Deviation Concept 

Standard Deviation is a statistical measure of dispersion. It is the under root of average squared deviations around mean.

Low standard deviation implies less spread and higher standard deviation implies more spread.

  • So, Distribution with higher standard deviation 2 and mean 1 has more spread than distribution with lower standard deviation 1 and mean 2.
03

True / False 

A]False : As the distribution with standard deviation 2 has more spread, so the distributions' spread are unequal

B] False : The distributions have different mean, 1 and 2 respectively. So, their centres are not same.

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Most popular questions from this chapter

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 -2.55 and -2.00.

In Exercises 7鈥�10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Standard Deviation For the following, round results to three decimal places.

a. Find the value of the population standard deviation

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample standard deviation s. Then combine values of s that are the same, as in Table 6-3 (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)

c. Find the mean of the sampling distribution of the sample standard deviation. d. Based on the preceding results, is the sample standard deviation an unbiased estimator of the population standard deviation? Why or why not?

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.

Critical Values. In Exercises 41鈥�44, find the indicated critical value. Round results to two decimal places.

z0.02

Standard normal distribution, 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.

Greater than -3.75
See all solutions

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