Question

Assume that in the Innovative Speaker simulation, the standard deviation of 1000 trials was 8404 and the mean was 16,808, as shown below. What are the chances that the actual cashflow could still be negative? Express your answer as a decimal with 3 decimal places. For example, 50% should be written as .500

Answer 1

Answer:

P(net flow to be negative) = 0.023

Step-by-step explanation:

Given:

Standard deviation (SD) of 1000 trials = 8404

Mean = 16,808

To find:

Probability of actual negative cashflow (expresses as a decimal with 3 decimal places)

Solution:

For the cash flow to be negative the value needs to be as follows:

Net cash flow = < Mean - 2*standard deviation

Thus,

Let net flow be denoted by X

Then X => mean - 2*standard deviation = 16808-2*8404 = 0

Z score = (X - Mean) / Standard deviation

Z score = (0 - 16808)/8404 = -2

Hence we need to find the P(Z < -2)

as per the normal distribution , we refer to the Z table, attached below.

The P( Z< -2) = 0.0228

Hence the correct answer rounded off is P(net flow to be negative) = 0.023

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