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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset Vaia Explanations$ Math

OER 2018 Edition · 902 pages

ISBN: 9781938168208

Chapter 7: Q.34 (page 429)

What is the mean of ΣX?

Short Answer

Expert verified

The mean of $\sum X$ is 10000

Step by step solution

Given Information

According to the Given details, the mean of the unknown distribution is 100, the standard deviation is 100 and the sample size is 100 objects of interest.

Explanation

Then the mean of $\sum X$ is given as:

$= (n) (μ_{X})$

$= 100 \times 100$

$= 10000$

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Most popular questions from this chapter

M&M candies large candy bags have a claimed net weight of $396.9$ g. The standard deviation for the weight of the

individual candies is $0.017$ g. The following table is from a stats experiment conducted by a statistics class.

Red	Orange	Yellow	Brown	Blue	Green
$0.751$	$0.735$	$0.883$	$0.696$	$0.881$	$0.925$
$0.841$	$0.895$	$0.769$	$0.876$	$0.863$	$0.914$
$0.856$	$0.865$	$0.859$	$0.855$	$0.775$	$0.881$
$0.799$	$0.864$	$0.784$	$0.806$	$0.854$	$0.865$
$0.966$	$0.852$	$0.824$	$0.840$	$0.810$	$0.865$
$0.859$	$0.866$	$0.858$	$0.868$	$0.858$	$1.015$
$0.857$	$0.859$	$0.848$	$0.859$	$0.818$	$0.876$
$0.942$	$0.838$	$0.851$	$0.982$	$0.868$	$0.809$
$0.873$	$0.863$			$0.803$	$0.865$
$0.809$	$0.888$			$0.932$	$0.848$
$0.890$	$0.925$			$0.842$	$0.940$
$0.878$	$0.793$			$0.832$	$0.833$
$0.905$	$0.977$			$0.807$	$0.845$
	$0.850$			$0.841$	$0.852$
	$0.830$			$0.932$	$0.778$
	$0.856$			$0.833$	$0.814$
	$0.842$			$0.881$	$0.791$
	$0.778$			$0.818$	$0.810$
	$0.786$			$0.864$	$0.881$
	$0.853$			$0.825$
	$0.864$			$0.855$
	$0.873$			$0.942$
	$0.880$			$0.825$
	$0.882$			$0.869$
	$0.931$			$0.912$
				$0.887$

The bag contained $465$ candies and the listed weights in the table came from randomly selected candies. Count the weights.

a. Find the mean sample weight and the standard deviation of the sample weights of candies in the table.

b. Find the sum of the sample weights in the table and the standard deviation of the sum of the weights.

c. If $465$ M&Ms are randomly selected, find the probability that their weights sum to at least $396.9$ .

d. Is the Mars Company’s M&M labeling accurate?

The length of songs in a collector’s iTunes album collection is uniformly distributed from two to $3.5$ minutes. Suppose we randomly pick five albums from the collection. There are a total of $43$ songs on the five albums.

a. In words, $Χ =_________$

b. $Χ ~_____________$

c. In words, $X =_____________$

d. $X ~_____(_____,_____)$

e. Find the first quartile for the average song length, $X$ .

f. The IQR (interquartile range) for the average song length, $X$ , is from ___ - ___.

Find the percentage of sums between $1.5$ standard deviations below the mean of the sums and one standard deviation above the mean of the sums.

In a city, $46$ percent of the population favor the incumbent, Dawn Morgan, for mayor. A simple random sample of $500$ is taken. Using the continuity correction factor, find the probability that at least $250$ favor Dawn Morgan for mayor.

An unknown distribution has a mean of $100$ , a standard deviation of $100$ , and a sample size of $100$ . Let $X =$ one object of interest.

What is $P (Σ x > 9, 000)$ ?

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What is the mean of ΣX?

Short Answer

Step by step solution

Given Information

Explanation

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