Question

The profit (or loss) from an investment is normally distributed with a mean of $11,200 and a standard deviation of $8,250. Find x such that the probability that the profit will exceed x is 25%. Group

Answer 1

The value of x such that the probability that the profit will exceed x is 25% is $17,534.05.

Step-by-step explanation:

To find x such that the probability that the profit will exceed x is 25%, we need to find the z-score corresponding to a cumulative probability of 0.75 (1 - 0.25).

The z-score can be found using the z-score formula: z = (x - mean) / standard deviation.

Rearranging the formula, we get x = (z * standard deviation) + mean.

Substituting the values given, we have z = 0.674 and mean = 11,200 and standard deviation = 8,250.

Plugging in these values, we can solve for x:

x = (0.674 * 8250) + 11200 = 17534.05

Therefore, the value of x such that the probability that the profit will exceed x is 25% is $17,534.05.