Question

Suppose that you are a student worker in the statistics department and they agree to pay you using the random pay system. Each week, the Chair flips a coin. If it comes up heads, your pay for the week is $80 and if it comes up tails your pay for the week is $40. Your friend is working for the engineering department and makes $65 per week. The probability that your total earnings in 100 weeks are more than hers is approximately...?

Answer 1

Answer:

The probability of getting paid more than $6500 in 100 weeks is 0.6%

Explanation:

In this problem, we need to define a probabilty distribution for the money earned.

The 100-week payoff can be expressed as

$PO=40*L+80*H=40*(100-H)+80*H=4000+40H$

Being L the numbers of weeks we have low pay and H the weeks we have high pay.

Now, as it is a coin flip, H is a binomial random variable with p=0.5 and n=100

For a total pay off of more than 6500, H has to be

$6500=4000+40H\\\\H=2500/40=62.5$

That means that in at least 63 of the 100 weeks we have to get a high pay.

$P(H\geq 63)=1-\sum_{i=1}^{62} P(X_i)$

If we compute the individual probabilities we get P(H≥63)=0.006 or 0.6%.