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 $143.311 and standard deviation of $3.9988 Approximately 38.34% of days IBM had a stock price greater than what dollar amount

Answer 1

Greater than $144.49.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of $143.311 and standard deviation of $3.9988.

This means that
`\mu = 143.311, \sigma = 3.9988`.

Approximately 38.34% of days IBM had a stock price greater than what dollar amount?

Greater than X when Z has a p-value of 1 - 0.3834 = 0.6166, so X when Z = 0.295.

`Z = (X - \mu)/(\sigma)`

`0.295 = (X - 143.311)/(3.9988)`

`X - 143.311 = 0.295*3.9988`

`X = 144.49`

Greater than $144.49.