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Chapter 6: Q. 6.5 (page 268)

Why is the standard normal curve sometimes referred to as the z-curve?

Short Answer

Expert verified

The standard normal curve sometimes referred to as the z-curve. This is because,

  • While drawing this standard normal curve, we label the horizontal axis as z.
  • Also refer to numbers on that axis asz-scores.

Step by step solution

01

Step 1. Given information

We need to explain why the standard normal curve sometimes referred to as thez-curve.

02

Step 2. Explanation for the answer:

The standard normal curve sometimes referred to as the z-curve. This is because:

  • The standard normal curve is the associated normal curve which is for a standardized normally distributed variable.
  • While drawing that curve, we label the horizontal axis with a letter z.
  • Also, we refer the numbers on that axis as z-scores.
03

Step 3. The model pictorial representation of the standard normal curve:

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Most popular questions from this chapter

20. Sketch the normal curve having the parameters

a. μ=-1andσ=2

b. μ=3andσ=2

c. μ=-1andσ=0.5

A variable is normally distributed with a mean of 0 and standard deviation 4. Find the percentage of all possible values of the variable.

a. lie between -8 and 8 .

b. exceed -1.5,

c. are less than 2.75.

We have provided a normal probability plot of data from a sample of a population. In each case, assess the normality of the variable under consideration.

Female College Students. Refer to Example 6.3 on page 256 .

a. Use the relative-frequency distribution in Table 6.1 to obtain the percentage of female students who are between 60and65inches tall.

b. Use your answer from part (a) to estimate the area under the normal curve having parameters μ=64.4andσ=2.4that lies between 60and65. Why do you get only an estimate of the true area?

13. What key fact permits you to determine percentages for a normally distributed variable by first converting to z-scores and then determining the corresponding area under the standard normal curve?
See all solutions

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