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# Change of earning $380 a week

Posted on 2012-09-13

Ok based on the answer to the linked question, let me check I've understood this.

First a recap of the original question.

Each job pays $10 on average with a sd of $1.50.

I get a maximum of 70 jobs a week.

What is the probability I'll earn $800 in a week?

Answer:

Get the average income based on 70 jobs: 70 x $10 = $700.

Take the original sd 1.5 and square it: 2.25.

Multiply that by the number of jobs - 70 = 157.5.

Take the square root of that: $12.55.

Now work out the size of the increase to make $800: $800 - $700 = $100.

Divide that my the new sd: 100/12.55 = 7.968

Try to look that up in a normal distribution and it is off the scale, so it is very unlikely you will earn $800 in a week.

Now given that, here is a new question:

A job pays $5.67 with an sd of $1.96.

There is a maximum of 65 customers a week.

What is the probability of earning $380.

65 x 5.67 = 368.55

1.96^2=3.8416 x 65 = 249.704

sqrt(249.704) = 15.802

380 - 368.55 = 11.45

11.45 / 15.802 = 0.7246

Look this up in the normal distribution and you get a probability of 76.42%.

This is the probability of making at least $380 in a week.

Is this correct?