Question

6. The monthly income of residents of small town is normally distributed with a mean of $3000 and a standard deviation of $500. a. The mayor of small town makes $2,250 a month. What percentage of small town's residents has incomes that are more than the mayor's? b. Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes? c. What are the minimum and the maximum incomes of the middle 95% of the residents? d. Two hundred residents have incomes of at least $4,440 per month. What is the population of small town? Briefly discuss your results.

          6. The monthly income of residents of small town is normally distributed with a mean of $3000 and a standard deviation of $500.
a.
The mayor of small town makes $2,250 a month. What percentage of small town's residents
has incomes that are more than the mayor's?
b. Individuals with incomes of less than $1,985 per month are exempt from city taxes. What
percentage of residents is exempt from city taxes?
c.
What are the minimum and the maximum incomes of the middle 95% of the residents?
d. Two hundred residents have incomes of at least $4,440 per month. What is the population of
small town? Briefly discuss your results.

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6. The monthly income of residents of small town is normally distributed with a mean of 3000 and a standard deviation of500.
a.
The mayor of small town makes 2,250 a month. What percentage of small town's residents
has incomes that are more than the mayor's?
b. Individuals with incomes of less than1,985 per month are exempt from city taxes. What
percentage of residents is exempt from city taxes?
c.
What are the minimum and the maximum incomes of the middle 95% of the residents?
d. Two hundred residents have incomes of at least 4,440 per month. What is the population of
small town? Briefly discuss your results.

Added by Kelly G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Donna Densmore

03/23/2023

Step 1

We need to find the percentage of residents with incomes more than the mayor's ($2,250). To do this, we'll first find the z-score for the mayor's income: $z = \frac{X - \mu}{\sigma} = \frac{2250 - 3000}{500} = -1.5$ Now, we'll use the z-table or a calculator to Show more…

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The monthly income of residents of small town is normally distributed with a mean of $3000 and a standard deviation of $500. a. The mayor of small town makes $2,250 a month. What percentage of small town's residents has incomes that are more than the mayor's? b. Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes? c. What are the minimum and the maximum incomes of the middle 95% of the residents? d. Two hundred residents have incomes of at least $4,440 per month. What is the population of small town? Briefly discuss your results.

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Transcript

00:01 So we have a town that has a normally distributed salaries, and we need to find the following probabilities for a main of 3 ,000 standard deviation of 500.

00:14 So we need to find our z scores for 2250 and 1985.

00:19 So i can get my formula.

00:20 My z score would be 2250 minus the 3 ,000, over 500.

00:26 And then for the next one, i'm going to go my z score would be 1985 minus 3 ,000.

00:31 Thousand over 500.

00:34 So let's get those numbers.

00:36 So that's going to be for the first one.

00:39 Let me get to the right screen.

00:42 We're going to have a z score of negative 1 .5 for the second one.

00:52 A z score of negative 2 .03.

00:55 So what we need to do is go to our z table and find those.

00:58 I'm not going in any particular order.

01:00 I just happen to see the negative 2 .03 first.

01:04 So this is going to be 0 .021.

01:08 118 and since we're less than that's going to be our answer.

01:12 So let me go find negative 1 .5.

01:15 That's going to be 0 .06681.

01:20 Since that's greater than i need to subtract that from one so let's go do that real quick.

01:28 And i'm going to get a value of 0 .93319.

01:32 Now i want to know the max and min value for 95%.

01:36 Well since this is normally distributed we can use the fact that 95 % are within two standard deviations...

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