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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

Without consulting Table II, explain why the area under the standard normal curve that lies to the right of 0 is 0.5.

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.

Determine the two z-scores that divide the area under the standard normal curve into a middle 0.90 area and two outside 0.05areas.

Arterial Cord path. Umbilical cord blood analysis immediately after delivery is one way to measure the health of an infant after birth. Researchers G. Natalucci et al used it as a predictor of brain maturation of preterm infants in the article "Functional Brain

Maturation Assessed During Early Life Correlates with Anatomical Brain Maturation at Term-Equivalent Age in Preterm Infants " (Proly. are Resend, Vol. 74. No. 1. pp. 68-74). Based on this study. we will assume that, for preterm infants, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with a mean of 7.32 and a standard deviation of 0.1. Find the percentage of preterm infants who have arterial cord pH levels

a. between 7.0 and 7.5.

b. over 7.4.

12. Consider the normal curves that have the parameters 渭=1.5and 蟽=3;渭=1.5and 蟽=6.2;渭=-2.7and 蟽=3;渭=0and蟽=1.

a. Which curve has the largest spread?

b. Which curves are centered at the same place?

c. Which curves have the same spread?

d. Which curve is centered farthest to the left?

e. Which curve is the standard normal curve?蟽
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