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Foreign-born residents Refer to Exercise 11 Here are summary statistics for

the percent of foreign-born residents in the 50 states:

a. Find and interpret the z-score for Montana, which had 1.9% foreign-born residents.

b. New York had a standardized score of 2.10 Find the percent of foreign-born residents in New York at that time.

Short Answer

Expert verified

Part (a) Montana's percentage of foreign-born residents is 1.12standard deviations lower than the national average of foreign-born residents.

Part (b) New York has approx. 21.582%of foreign born residents.

Step by step solution

01

Part (a) Step 1: Given information

The table is

nMeanSDMinQ1
MedQ3
Max
508.736.121.34.16.213.427.1

Value, x=1.9

Mean, x=8.73

Standard deviation, SD=6.12

02

Part (a) Step 2: Concept

The formula used:z=valuemeanstandarddeviation

03

Part (a) Step 3: Calculation

The amount of standard deviations a value deviates from the mean is represented by the z-score.

A positivez-score implies a value that is higher than the mean.

Whereas,

When the z-score is negative, it means the value is below the mean.

Calculate the zscore:

z=xxSD=1.98.736.12=6.836.121.12

Therefore,

Montana's percentage of foreign-born residents is 1.12standard deviations lower than the national average of foreign-born residents.

04

Part (b) Step 1: Calculation

The amount of standard deviations a value deviates from the mean is represented by the z-score.

A positivez-score implies a value that is higher than the mean.

Whereas,

When the z-score is negative, it means the value is below the mean.

Calculate thezscore:

z=xxSD

Substitute the values:

2.10=x8.736.12

Multiply both sides by 6.12:

12.852 = x 鈭 8.73

Add 8.73to both sides:

12.852+8.73=x8.73+8.73

That becomes

x=21.582

Therefore,

New York has approx. 21.582%of foreign based residents.

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