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?
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?