Question

The daily stock price for International Business Machines (IBM) historically has followed an approximately normal distribution (when adjusting for inflation) with a mean of $133.654 and standard deviation of $3.9212 Approximately 79.88% of days IBM had a stock price less than what dollar amount?

Answer 1

Solution:

Let X be a random variable which represents the daily stock price for IBM.

Give that,

i.e. μ = 133.654 and σ = 3.9212

Let approximately 79.88% of days IBM had a stock price less than the amount x dollars.

Hence, P(X < x) = 0.7988

We know that, if then,  

..............................(1)

Using Z-table we get, P(Z < 0.8374) = 0.7988

Comparing P(Z < 0.8374) = 0.7988 and expression given in (1) we get,

  

Hence, approximately 79.88% of days IBM had a stock price less than the amount $136.9376.