Question

Assume the given distributions are roughly normal. The mean income per household in a certain state is $\$ 9500$ with a standard deviation of $\$ 1750 .$ The middle $95 \%$ of incomes are between what two values? (A) $9500 \pm 1.645(1750)$ (B) $9500 \pm 1.96(1750)$ (C) $9500 \pm 1.645\left(\frac{1750}{2}\right)$ (D) $9500 \pm \frac{1750}{1.645}$ (E) $9500 \pm \frac{1750}{1.96}$

Name: Problem 5, Chapter 5: AP Statistics with 6 Practice Tests
Uploaded: 2021-04-16T23:22:37-08:00
Duration: 1 min 42 s
Channel: Jerrah Biggerstaff
Description: Assume the given distributions are roughly normal. The mean income per household in a certain state is 9500 with a standard deviation of 1750 . The middle 95 % of incomes are between what two values? (A) 9500 ±1.645(1750) (B) 9500 ±1.96(1750) (C) 9500 ±1.645((1750)/(2)) (D) 9500 ±(1750)/(1.645) (E) 9500 ±(1750)/(1.96)

   Assume the given distributions are roughly normal.
The mean income per household in a certain state is $\$ 9500$
with a standard deviation of $\$ 1750 .$ The middle $95 \%$ of incomes are between what two values?
(A) $9500 \pm 1.645(1750)$
(B) $9500 \pm 1.96(1750)$
(C) $9500 \pm 1.645\left(\frac{1750}{2}\right)$
(D) $9500 \pm \frac{1750}{1.645}$
(E) $9500 \pm \frac{1750}{1.96}$

AP Statistics with 6 Practice Tests

Martin Sternstein 11th Edition

Chapter 5, Problem 5

Instant Answer

Solved by Expert Jerrah Biggerstaff

04/16/2021

Step 1

96 standard deviations of the mean. This is a standard rule in statistics. Show more…

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Assume the given distributions are roughly normal. The mean income per household in a certain state is $\$ 9500$ with a standard deviation of $\$ 1750 .$ The middle $95 \%$ of incomes are between what two values? (A) $9500 \pm 1.645(1750)$ (B) $9500 \pm 1.96(1750)$ (C) $9500 \pm 1.645\left(\frac{1750}{2}\right)$ (D) $9500 \pm \frac{1750}{1.645}$ (E) $9500 \pm \frac{1750}{1.96}$

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Key Concepts

Normal Distribution

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. This distribution is characterized by its bell shape and is defined by its mean and standard deviation, with the properties of the distribution remaining consistent regardless of the specific data values.

Z-Score and Confidence Intervals

A z-score represents the number of standard deviations a data point is from the mean in a normal distribution. For calculating confidence intervals, especially when data is assumed to be normally distributed, critical z-values are used. For example, the middle 95% of the data in a normal distribution corresponds approximately to z-scores of ±1.96, which, when multiplied by the standard deviation and added to the mean, give the boundaries of the confidence interval.

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