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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 7: Q.AP2.19 - Cumulative AP Practise Test (page 438)

When people order books from a popular online source, they are shipped in boxes.
Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5 pound with a standard deviation of 0.1 pound, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?
a. 1.84
b. 2.60
c. 3.02
d. 3.40
e. 9.10

Short Answer

Expert verified

c. 3.02

Step by step solution

01

Given Information

$ver (total) = var (A) + var (B) + var$ (C)

A= Weight of boxes

B= weight of packing

C= weight of boxes

Formula used:

02

Explanation for correct option

$ver (total) = 0 . 3^{2} + 0 . 1^{2} + 3^{2} = 9.1 S D = \sqrt{9.1} = 3.02$

Hence, the correct option is (c)

03

Explanation for incorrect option

a. 1.84 is not the correct answer.

b. 2.60 is not the correct answer.

d. 3.40 is not the correct answer.

e. 9.10 is not the correct answer.

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Most popular questions from this chapter

Cold cabin? The dotplot shows the results of taking $300$ SRSs of $10$ temperature readings from a Normal population with $μ^{μ} = 50$ and $σ^{σ} = 3$ and recording the sample standard deviation $s x^{s_{x}}$ each time. Suppose that the standard deviation from an actual sample is $s x = 5 ° F .^{s x = 5 ° F}$ . What would you conclude about the thermostat manufacturer's claim? Explain your reasoning.

Dead battery? A car company claims that the lifetime of its batteries varies from car to car according to a Normal distribution with mean $μ = 48$ months and standard deviation $σ = 8 .2$ months. A consumer organization installs this type of battery in an SRS of 8 cars and calculates $\bar{x} = 42 .2$ months.

a. Find the probability that the sample mean lifetime is 42.2 months or less if the company's claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average lifetime of its batteries?

Exercises 77 refer to the following setting. In the language of government statistics, you are "in the labor force" if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) that is unemployed. Here are estimates from the Current Population Survey for the civilian population aged 25 years and over in a recent year. The table entries are counts in thousands of people.

Unemployment (1.1) Find the unemployment rate for people with each level of education. Is there an association between unemployment rate and education? Explain your answer.

Suppose we roll a fair die four times. What is the probability that a 6 occurs on exactly one of the rolls?

$a . 4 (16) 3 (56) 14 {(\frac{1}{6})}^{3} {(\frac{5}{6})}^{1} b . (16) 3 (56) 1 {(\frac{1}{6})}^{3} {(\frac{5}{6})}^{1} c . 4 (16) 1 (56) 3 {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3} d . (16) 1 (56) 3 {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3} e . 6 (16) 1 (56) 3^{6} {(\frac{1}{6})}^{1} {(\frac{5}{6})}^{3}$

Sample minimums List all $6$ possible SRSS of size $n = 2$ , calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dotplot. Is the sample minimum an unbiased estimator of the population minimum? Explain your answer.

COLOR	AGE
RED	$1$
WHITE	$5$
SILVER	$8$
RED	$20$

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