T2.2. For the Normal distribution shown, the standard deviation is closest to

(a) 0

(b) 1

(c) 2

(d) 4

(e) 5

Short Answer

Expert verified

Option (d) 4

Step by step solution

01

Concept Introduction (Part a)

Standard deviation describes how far values vary from the mean of the set, while a high standard deviation indicates a more wide-ranging variation. A low standard deviation indicates closeness to the mean, while a high standard deviation indicates the values are spread out over a larger range.

02

Explanation 

We observe that the normal distribution peak is at about 4. This means that the mean is at the peak of the normal distribution.

μ4

This distance from μ=4to inflection point (where the curve appears approximately straight) is the standard deviation of the normal distribution.

Therefore, the standard deviation in this case is 4 (i.e.). In this case, the distance is about 4 and the standard deviation is approximately 4.

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Most popular questions from this chapter

Python eggs (1.1) How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers assigned newly laid eggs to one of three temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs and the number that hatched:

(a) Make a two-way table of temperature by outcome (hatched or not).

(b) Calculate the percent of eggs in each group that hatched. The researchers believed that eggs would not hatch in cold water. Do the data support that belief?

T2.3. Rainwater was collected in water collectors at 30different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1pHunits to all of the values and then multiplying the result by 1.2. The mean and standard deviation of the corrected pH measurements are

(a)5.64,1.44

(b)5.64,1.32

(c)5.40,1.44

(d)5.40,1.32

(e)5.64,1.20

R2.12 Assessing Normality A Normal probability plot of a set of data is shown here. Would you say that these measurements are approximately Normally distributed? Why or why not?

Blood pressure Larry came home very excited after a visit to his doctor. He announced proudly to his wife, “My doctor says my blood pressure is at the 90thpercentile among men like me. That means I’m better off than about 90% of similar men.” How should his wife, who is a statistician, respond to Larry’s statement?

R2.7 Standard Normal areas Use Table A to find the proportion of observations from a standard Normal distribution that falls in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.

(a) z-2.25

(b)z-2.25

(c) role="math" localid="1649401025226" z>1.77

(d) -2.25<z<1.77

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