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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.10 (page 428)

Find the sum that is $1.5$ standard deviations below the mean of the sums.

Short Answer

Expert verified

The sum is $\sum X = 7424.5577$ .

Step by step solution

01

Given Information

A sample size $(n) = 95$ .

The mean of population $(μ_{X}) = 80$ .

$z = 1.5$

A standard deviation $(σ_{X}) = 12$ .

02

Explanation

To find the sum that is $1.5$ standard deviation below the mean of the sums:

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

Calculating, we have:

$\sum X = 95 \times 80 - 1.5 \times \sqrt{95} \times 12$

$\sum X = 7424.5577$

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Most popular questions from this chapter

Find the probability that the average price for $30$ gas stations is less than $$ 4.55$ .

a. $0.6554$

b. $0.3446$

c. $0.0142$

d. $0.9858$

e. $0$

Find the sum that is one standard deviation above the mean of the sums.

Find the probability that the sums will fall between the $z -$ scores $- 2$ and $1$ .

Find the probability that the sample mean is between seven and 11

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?

See all solutions

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