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

Answer:

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

Step-by-step 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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

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

$P(186.26 \leq x \leq 192.47) = P(\displaystyle\frac{186.26 - 188.876}{4.6412} \leq z \leq \displaystyle\frac{192.47-188.876}{4.6412}) = P(-0.5636 \leq z \leq 0.7743)\\\\= P(z \leq 0.7743) - P(z < -0.5636)\\= 0.781 - 0.287 = 0.494 = 49.4\%$

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

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