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Chapter 6: Q. 6.86 (page 276)

Briefly, for a normally distributed variable, how do you obtain the percentage of all possible observations that lie within a specified range?

Short Answer

Expert verified

Step 1: The connected variable's normal curve is drawn.

Step 2: The region of interest is shaded, and the x-value(s) noted

Step 3: The z-score(s) are calculated.

Step 4: Using the standard normal table, get the area under the standard normal curve.

Step by step solution

01

Concept introduction

The quantity of one variable in algebraic equations is typically reliant on the position of another. If the data tuple isn't declared precisely, the variable's beginning value reflects the default value.

02

Explanation

First, determine the equivalent area under the standard normal curve by expressing the range in terms of z-scores.

The steps are as follows:

Step 1: The connected variable's normal curve is drawn.

Step 2: The region of interest is shaded, and the x-value(s) that define it are noted.

Step 3: Calculate the z-score(s) for the delimiting x-value(s).

Step 4: Using the standard normal table, get the area under the standard normal curve delimited by the z-score(s).

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Most popular questions from this chapter

From the paper "Effects of Chronic Nitrate Exposure on Gonad Growth in Green Sea Urchin Strongylocentrotus droebachiensis" by S. Siikavuopio et al., we found that weights of adult green sea urchins are normally distributed with mean 52gand standard deviation 17.2g.

Part (a): Find the percentage of adult green sea urchins with weights between 50gand 60g.

Part (b): Obtain the percentage of adult green sea urchins with weight above 40g.

Part (c): Determine and interpret the 90thpercentile for the weights.

Part (d): Find and interpret the 6thdecile for the weights.

Use Table to obtain the areas under the standard normal curve. Sketch a standard normal curve and shade the area of interest in each problem.

Find the area under the standard normal curve that lies

a. either to the left of -2.12or to the right of 1.67.

b. either to the left of 0.63or to the right of 1.54.

Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also show that the mean time between arriving patients is 8.78 minutes.

a. Use the technology of your choice to simulate four random samples of75 interarrival times each.

b. Obtain a normal probability plot of each sample in part (a).

c. Are the normal probability plots in part (b) what you expected? Explain your answer.

6.68 Use Table II to obtain each shaded area under the standard normal curve.

The National Center for Health Statistics publishes information about birth rates (per 1000population) in the document National Vital Statistics Report. The following table provides a frequency distribution for birth rates during one year for the 50states and the District of Columbia

a. Obtain a frequency histogram of these birth-rate data.

b. Based on your histogram, do you think that birth rates for the 50states and the District of Columbia are approximately normally distributed? Explain your answer.
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