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Chapter 2: Q.45 (page 131)

Estimating SD The figure at top right shows two Normal curves, both with mean 0. Approximately what is the standard deviation of each of these curves?

Short Answer

Expert verified

The standard deviation is approximately (0.6)-(-0.6)6=0.2for the tall, more concentrated one. And (1.5)-(-1.5)6=0.5for the short.

Step by step solution

01

Given Information

It is given in the question that, the figure shows two Normal curves, both with a mean of 0.

02

Step 2: Explanation

According to the graph, a normal distribution has a range of values of about six standard deviations.

This tall, concentrated one has a standard deviation of approximately (0.6)-(-0.6)6=0.2and the short, less concentrated one has a standard deviation of approximately(1.5)-(-1.5)6=0.5

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Most popular questions from this chapter

Use Table A to find the value zfrom the standard Normal distribution that satisfies each of the following conditions. In each case, sketch a standard Normal curve with your value of zmarked on the axis. Use your calculator or the Normal Curve applet to check your answers.

Working backward

(a) The 10th percentile.

(b) 34% of all observations are greater thanz.

Which of the following is least likely to have a nearly Normal distribution?

(a) Heights of all female students taking STAT 001 at State Tech.

(b) IQ scores of all students taking STAT 001 at State Tech.

(c) SAT Math scores of all students taking STAT 001 at State Tech.

(d) Family incomes of all students taking STAT 001 at State Tech.

(e) All of (a)–(d) will be approximately Normal.

R2.9 low-birth-weight babies Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year period. The distribution of birth weights is Normal with a mean of 3668 grams and a standard deviation of 511 grams. 17 Babies that weigh less than 2500 grams at birth are classified as "low birth weight."

(a) What percent of babies will be identified as having low birth weight? Show your work.

(b) Find the quartiles of the birth weight distribution. Show your work.

T2.6. The figure shown is the density curve of a distribution. Five of the seven points marked on the density curve make up the five-number summary for this distribution. Which two points are not part of the five-number summary?

(a) Band E
(b) C and F
(c) C and E
(d) B and F
(e) A and G.

Growth charts We used an online growth chart to find percentiles for the height and weight of a 16-year-old girl who is 66 inches tall and weighs 118 pounds. According to the chart, this girl is at the 48th percentile for weight and the 78th percentile for height. Explain what these values mean in plain English.
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