Board 8 > Who wants to help me with my math test?

(+) Yeah! (+)

Suppose a study of the income of graduation students shows that 5 years after graduation, the students' income is normally distributed with a mean of $41,600 and a standard deviation of $12,500.

(i) What is the probability a student will have an income higher than $50,000?

(ii) What is the probability that a student's income will be between $20,000 and $60,000?

This isn't for the actual test. These are review problems. I just need to know how to set these up/the equation for setting these up.

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I'm not sure how your probability course is set up, but mine came with a little chart of z-scores. Set 41,600 to 0, then calculate how many standard deviations 50,000 is away from the mean. Then consult your chart of z-scores to see the probability that it would be higher than that many standard deviations away.

Part 2 would be similarly calculated, just a few more steps at the end.

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Uhhh...use a calculator

(i) normalcdf (50000, some high number like 10^6, 41600, 12500)
= 0.251

(ii) normalcdf (20000, 60000, 41600, 12500)
= 0.887

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Balls. Used a mean of 50000 for part ii.

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Of course, you could use z-values, but who wants to do it that way when you have access to a calculator anyway?

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i. 50000 - 41600 = 8400
8400/12500 = .672
Looking at a normal distribution table for .67 => .2514

ii. 41600 - 20000 = 21600; 60000 - 41600 = 18400
21600/12500 = 1.728; 10000/12500 = 1.472
Table for 1.73 => .0418; Table for 1.47 => .0708
1 - .0708 = .9292
.9292 - .0418 = .8874

EDIT: Fix'd

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From: kurtfisto | #006
Of course, you could use z-values, but who wants to do it that way when you have access to a calculator anyway?

In any stat exam I've taken, you had to show work for the z-scores and stuff.

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Thanks team. Hopefully I remember this come test time. Been overwhelmed this weekend with work and put off studying.

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