Question

A stock's price fluctuations are approximately normally distributed with a mean of $104.50 and a standard deviation of $23.62. You decide to purchase whenever the price reaches its lowest 10% of values. What is the most you would be willing to pay for the stock?

Answer 1

$ 74.23

Step-by-step explanation:

We are given the following:

mean, μ = $ 104.50

standard deviation, σ = $ 23.62

Using the z-score table, we have

P(Z < z) = 10% (since we are evaluating lowest 10% of values)

hence P(Z < z) = 0.10

P(Z < -1.282 ) = 0.10

z = -1.282 (this evaluates to 0.1 on the z-score table)

Using z-score formula,

x = z *σ + μ

substituting the values,

x =- - 1.282 * 23.62 + 104.50

= 74.23

The most for the stock is $ 74.23