Suppose that you are a student worker in the Accounting Department of the Busine

Question

Suppose that you are a student worker in the Accounting Department of the Business School 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 exist80: if it comes up tails your pay for the week is exist40. Your friend is working for the Engineering Department and makes exist65 per week. The probability that your earnings in each week during 100 weeks are more than hers (=exist65) is approximately: 1. Find the expected value of your pay (mu) X_i (Payment) Probability (P_i) 2. Based on the above, calculate a standard deviation of your pay sigma = 3. Applying z-score formula with understanding of your variable (is it for individual payment or for the sample mean of payments?) 4. Find the probability

Explanation / Answer

Solution:-

Probability of getting heads = 1/2 = 0.5, thereby earning $ 80.

Probability of getting tails = 1/2 = 0.5, thereby earning $ 40.

We can approach this one using proportions:

using algebra you can find that you need 62.5 heads and 37.5 tails to equal $65 a week.

Our population proportion is p = 0.5

= sqrt[p(1-p) / n]

= sqrt [0.5 (0.5) / 100]

= 0.05

P(p-hat > 0.625) = normalcdf (0.625, 1, 0.5, 0.05) = 0.0062

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