Question

The stock price for International Business Machines (IBM) historically has followed an approximately normal distribution (when adjusting for inflation) with a mean of $188.876 and standard deviation of $4.6412. What is the probability that on a selected day the stock price is between $186.26 and 192.47

Answer 1

0.494 is the probability that on a selected day the stock price is between $186.26 and $192.47.

Explanation:

We are given the following information in the question:

Mean, μ = $188.876

Standard Deviation, σ = $4.6412

We are given that the distribution of stock price is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(stock price is between $186.26 and $192.47)

`P(186.26 \leq x \leq 192.47) = P(\displaystyle(186.26 - 188.876)/(4.6412) \leq z \leq \displaystyle(192.47-188.876)/(4.6412)) = P(-0.5636 \leq z \leq 0.7743)\\\\= P(z \leq 0.7743) - P(z < -0.5636)\\= 0.781 - 0.287 = 0.494 = 49.4\%`

`P(186.26 \leq x \leq 192.47) = 49.4\%`

0.494 is the probability that on a selected day the stock price is between $186.26 and $192.47.