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Chapter 6: Q. 1 (page 286)

What is a density curve, and why are such curves important?

Short Answer

Expert verified

The total probability under the density curve is equal to unity,

The probability distribution of body weights is depicted by the density curve above.

Step by step solution

01

Given Information 

The meaning of density curve and to give its importance.

02

Explanation 

Think about the density curve.

The probability is represented graphically by the density curve. Density curves come in a variety of shapes and sizes.

They don't have to be symmetrical.

In theory, it depicts the probability distribution of a continuous variable.

As a result, the probability curve is smooth. It can, however, be used to calculate the probability distribution of discrete variables.

The area beneath the density curve represents 100% of all probability.

As a result, the overall probability under the density curve is one.

The probability distribution of body weights is depicted by the density curve above .

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Most popular questions from this chapter

Sketch the normal distribution with

(a)渭=3;蟽=3(b)渭=1;蟽=3(c)渭=3;蟽=1

For the standard normal curve, find the z- score(s)

a. that has area 0.30 to its left.

b. that has area 0.10 to its right.

c. z0.025,z0.05,z0.01andz0.005.

d. that divide the area under the curve into a middle 0.99 area and two outside 0.005 areas

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.

A variable is normally distributed with mean 6and standard deviation 2.

Part (a): Determine and interpret the quartiles of the variable.

Part (b) Obtain and interpret the 85thpercentile.

Part (c) Find the value that 65%of all possible values of the variable exceed.

Part (d) Find the two values that divide the area under the corresponding normal curve into a middle area of 0.95and two outside areas of 0.025. Interpret your answer.

Explain in detail what a normal probability plot is and how it is used to assess the normality of a variable.
See all solutions

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