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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

Low Birth Weight The University of Maryland Medical Center considers “low birth weights” to be those that are less than 5.5 lb or 2495 g. Birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g (based on Data Set 4 “Births” in Appendix B).

a. If a birth weight is randomly selected, what is the probability that it is a “low birth weight”?

b. Find the weights considered to be significantly low, using the criterion of a birth weight having a probability of 0.05 or less.

c. Compare the results from parts (a) and (b).

Sampling Distribution Data Set 4 “Births” in Appendix B includes a sample of birth weights. If we explore this sample of 400 birth weights by constructing a histogram and finding the mean and standard deviation, do those results describe the sampling distribution of the mean? Why or why not?

In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Standard Normal DistributionIn Exercises 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 scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between -2.00 and 2.00.

Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone density 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 bone density test score corresponding to the given information. Round results to two decimal places.

Find P99, the 99th percentile. This is the bone density score separating the bottom 99% from the top 1%.
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