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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.20 (page 428)

Find the sum with a $z$ –score of $0.5$ .

Short Answer

Expert verified

The sum with a $z -$ score of $0.5$ is $\sum X = 3903.5$ .

Step by step solution

Given Information

A sample size $(n) = 100$ .

The mean of population $(μ_{X}) = 39.01$ .

$z = 0.5$ .

A standard deviation $(σ_{X}) = 0.5$ .

Exlpanation

To find the sum with a $z -$ score of $0.5$ :

\sum X = (n) (μ_{X}) + (z) (\sqrt{n}) (σ_{X})

Calculating, we have:

$\sum X = 100 \times 39.01 + 0.5 \times \sqrt{100} \times 0.5$

$\sum X = 3903.5$

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Most popular questions from this chapter

A uniform distribution has a minimum of six and a maximum of ten. A sample of $50$ is taken.

Find the third quartile for the sum.

The length of time a particular smartphone's battery lasts follows an exponential distribution with a mean of ten months. A sample of 64 of these smartphones is taken.

Find the IQR for the mean amount of time 64 batteries last.

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?

For the sums of distribution to approach a normal distribution, what must be true?

Suppose that the duration of a particular type of criminal trial is known to have a mean of $21$ days and a standard deviation of seven days. We randomly sample nine trials.

a. In words, $Σ X =______________$

b. $Σ X ~_____(_____,_____)$

c. Find the probability that the total length of the nine trials is at least $225$ days.

d. Ninety percent of the total of nine of these types of trials will last at least how long?

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Find the sum with a $z$ –score of $0.5$ .

Short Answer

Step by step solution

Given Information

Exlpanation

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Find the sum with a z–score of 0.5.

Short Answer

Step by step solution

Given Information

Exlpanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Geometry

Mechanics Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the sum with a $z$ –score of $0.5$ .