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Chapter 4: Q AP1.6. (page 277)

The figure below shows a Normal density curve. Which of the following gives the best estimates for the mean and standard deviation of this Normal distribution?

(a)μ=200,σ=50(d)μ=225,σ=25(b)μ=200,σ=25(e)μ=225,σ=275(c)μ=225,σ=50

Short Answer

Expert verified

The correct option is(c)μ=225,σ=50

Step by step solution

01

Given information

02

Concept

Observational research looks at people and assesses factors of interest without trying to affect their responses.

03

Calculation

The middle number on the x-axis around which the normal density curve is symmetrical is obtained since the curve is symmetrical about the mean. For this, a perpendicular from the curve's peak is drawn, cutting the x-axis at 225, the mean. 99.7%of the observations fell within this range. The area between 225and 375is 150since the curve is symmetrical.

μ=2253σ=375−225=150σ=50

As a result, the best estimates for the normal distribution's mean and standard deviation are:μ=225,σ=50

As a result, the solution is an option (c).

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Most popular questions from this chapter

The manager of a sports arena wants to learn more about the financial status of the people who are attending an NBA basketball game. He would like to give a survey to a representative sample of the more than 20,000 fans in attendance. Ticket prices for the game vary a great deal: seats near the court cost over \(100 each, while seats in the top rows of the arena cost \)25 each. The arena is divided into 30 numbered sections, from 101 to 130 Each section has rows of seats labeled with letters from A (nearest the court) to ZZ (top row of the arena).

3 Which would be a better way to take a cluster sample of fans: using the lettered rows or the numbered sections as clusters? Explain.

Random digits Which of the following statements are true of a table of random digits, and which are false? Briefly explain your answers.

(a) There are exactly four 0s in each row of 40 digits.

(b) Each pair of digits has a chance 1/100 of being 00

(c) The digits 0000 can never appear as a group

because this pattern is not random.

Systematic random sample Sample surveys often use a systematic random sample to choose a sample of apartments in a large building or housing units in a block at the last stage of a multistage sample. Here is a description of how to choose a systematic random sample. Suppose that we must choose 4 addresses out of 100 Because 100/4=25 we can think of the list as four lists of 25 addresses. Choose 1 of the first 25 addresses at random using Table D. The sample contains this address and the addresses 25,50, and 75 places down the list from it. If the table gives 13, for example, then the systematic random sample consists of the addresses numbered 13,38,63, and 88

(a) Use Table D to choose a systematic random sample of 5 addresses from a list of 200 Enter the table at line 120

(b) Like an SRS, a systematic random sample gives all individuals the same chance to be chosen. Explain why this is true. Then explain carefully why a systematic sample is not an SRS.

In an interesting experiment, researchers examined the effect of ultrasound on birth weight. Pregnant women participating in the study were randomly assigned to one of two groups. The first group of women received an ultrasound; the second group did not. When the subjects’ babies were born, their birth weights were recorded. The women who received the ultrasounds had heavier babies.

Was the experiment double-blind? Why is this important?

Sampling frame Refer to the previous exercise. It is more common in telephone surveys to use random digit dialing equipment that selects the last four digits of a telephone number at random after being given the exchange (the first three digits). Explain how this sampling method results undercover which could lead to bias.
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