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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 .31 (page 429)

What is the z-score for Σx = 840?

Short Answer

Expert verified

The z-score for Σx = 840 is approximately 26

Step by step solution

Given Information

Given that details, the sample size of customers is 400 with a mean of 3 and the standard deviation is $0.7$ . The sum of values is 840, so the $Z$ -score is given as:

Explanation

The sum of values is 840, so the $Z$ -score is given as:

$840 = 400 \times 3 + (z) \times \sqrt{400} \times 0.7$

$- 360 = 14.0 (z)$

$z = 25.714$

$z = 26$

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Most popular questions from this chapter

81. The $90 t h$ percentile sample average wait time (in minutes) for a sample of 100 riders is:

a. $315.0$

b. $40.3$

c. $38.5$

d. $65.2$

What three things must you know about distribution to find the probability of sums?

Four friends, Janice, Barbara, Kathy and Roberta, decided to carpool together to get to school. Each day the driver would be chosen by randomly selecting one of the four names. They carpool to school for $96$ days. Use the normal approximation to the binomial to calculate the following probabilities. Round the standard deviation to four decimal places.

a. Find the probability that Janice is the driver at most $20$ days.

b. Find the probability that Roberta is the driver more than $16$ days.

c. Find the probability that Barbara drives exactly $24$ of those $96$ days.

What is the mean of ΣX?

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?

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What is the z-score for Σx = 840?

Short Answer

Step by step solution

Given Information

Explanation

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