Question

A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. i) How many students earned more than $30,000? ii) How many students earned between $27,000 and $33,000? iii) How many students earned less than $22,500 Select one a) ii and iii are correct statement but not one b) i is a correct statement but not ii or iii c) i and ii are correct statement but not iii d) I , ii and iii are all correct statements e) i and iii are correct statements but not ii

          A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000.

i) How many students earned more than $30,000?

ii) How many students earned between $27,000 and $33,000?

iii) How many students earned less than $22,500
Select one
a) ii and iii are correct statement but not one
b) i is a correct statement but not ii or iii
c) i and ii are correct statement but not iii
d) I , ii and iii are all correct statements 
e) i and iii are correct statements but not ii

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Added by Christian O.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Donna Densmore

06/10/2023

Step 1

Since the mean is $30,000, and the distribution is symmetric, exactly 50% of the students will earn more than $30,000. So, 50% of 500 students is 250 students. ii) Show more…

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A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. i) How many students earned more than $30,000? ii) How many students earned between $27,000 and $33,000? iii) How many students earned less than $22,500 Select one a) ii and iii are correct statement but not one b) i is a correct statement but not ii or iii c) i and ii are correct statement but not iii d) I , ii and iii are all correct statements e) i and iii are correct statements but not ii

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Transcript

00:01 So we have 500 students.

00:02 We look at their normally distributed, their mean income is $30 ,000, and we have a standard deviation of $3 ,000.

00:10 So we want to know how many have income that's greater than $30 ,000, how many have income that's between $27 ,000 and $33 ,000, and then how many are less than $22 ,500.

00:25 So the first thing we're going to do is go get the the proportions or probabilities from our z table.

00:31 So this one, since it's the mean, it's going to be equal to 0 .5.

00:35 So we don't have to worry with that.

00:37 Now we need to get z scores for $27 ,000, $33 ,000, and $22 ,500.

00:42 So let's go get that real quick.

00:44 We're going to take our data point minus the mean over the standard deviation.

00:51 So i'm going to do that for $27 ,000, $33 ,000, and for $22 ,500.

00:59 So $22 ,000.

01:01 So this one i can do by hand.

01:08 So i'm just going to get that as a value of 1.

01:11 This one i can do by hand as negative 1.

01:16 And but this one, i'm not going to do that one by hand.

01:18 So let's go get a calculator for that one.

01:21 So let's see, $22 ,500 minus the $30 ,000, and then divide that by $3 ,000.

01:27 I'm going to get negative 2 .5.

01:30 So now i'm going to go to my z table, pull it up real quick, and let's go get those particular values.

01:36 So if i'm in my positive, so positive one is 0 .84134...

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