The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 魅影直播 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 6: Q. 104 (page 430)

In debt? Refer to Exercise 100.
a. Justify why D can be approximated by a normal distribution.
b. Use a normal distribution to estimate the probability that $30$ or more adults in the sample have more debt than savings.

Short Answer

Expert verified

The D is about regularly distributed
The resultant probability is $0.08$

Step by step solution

Part (a) Step 1: Given Information

Given:

Adult population is $(n) = 100$

The percentage of adults who owe more money than they saverole="math" localid="1653979441143" $(p) = 0.24$

Part (a) Step 2: Check that D is generally distributed for a reason.

Consider,

$n p = 100 (0.24) = 24 > 10 n (1 - p) = 100 (1 - 0.24) = 76 > 10$

Therefore, the D is about regularly distributed.

Part (b) Step 1: Given Information

Given:

Adult population is $(n) = 100$

The percentage of adults who owe more money than they save $(p) = 0.24$

Part (b) Step 2: calculate the likelihood that at least 30 persons in the sample have more debt than savings.

When 30 or more adults have more debt than savings, the likelihood is computed as follows:

$\begin{array}{rcl} P (X & 鈮� & 30) = P (Z 鈮� \frac{30 - 100 (0.24)}{\sqrt{100 (0.24) (1 - 0.24)}}) \\ = & P (Z 鈮� 1.405) \\ = & 1 - 0.920 \\ = & 0.08 \end{array}$

As a result, a probability of 0.08 is necessary.

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魅影直播

In debt? Refer to Exercise 100.
a. Justify why D can be approximated by a normal distribution.
b. Use a normal distribution to estimate the probability that $30$ or more adults in the sample have more debt than savings.

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Check that D is generally distributed for a reason.

Part (b) Step 1: Given Information

Part (b) Step 2: calculate the likelihood that at least 30 persons in the sample have more debt than savings.

One App. One Place for Learning.

Most popular questions from this chapter

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Mechanics Maths

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Statistics

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Study anywhere. Anytime. Across all devices.

魅影直播

In debt? Refer to Exercise 100.a. Justify why D can be approximated by a normal distribution.b. Use a normal distribution to estimate the probability that 30or more adults in the sample have more debt than savings.

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Check that D is generally distributed for a reason.

Part (b) Step 1: Given Information

Part (b) Step 2: calculate the likelihood that at least 30 persons in the sample have more debt than savings.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Statistics

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In debt? Refer to Exercise 100.
a. Justify why D can be approximated by a normal distribution.
b. Use a normal distribution to estimate the probability that $30$ or more adults in the sample have more debt than savings.