Answer:
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
and standard deviation
, the z-score of a measure X is given by:
![Z = (X - \mu)/(\sigma)](https://img.qammunity.org/2022/formulas/mathematics/college/bnaa16b36eg8ubb4w75g6u0qutzsb68wqa.png)
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
.
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)](https://img.qammunity.org/2022/formulas/mathematics/college/bnaa16b36eg8ubb4w75g6u0qutzsb68wqa.png)
![0.295 = (X - 143.311)/(3.9988)](https://img.qammunity.org/2022/formulas/mathematics/college/5edtrr30rybl4dq6d2te4dgzo6v7tpdvfi.png)
![X - 143.311 = 0.295*3.9988](https://img.qammunity.org/2022/formulas/mathematics/college/fl8sgssnstr5131qqbjpz4a9hsoq2v7gn1.png)
![X = 144.49](https://img.qammunity.org/2022/formulas/mathematics/college/v1mp2ajwmyk62suj94uoc9qan3pnknw3be.png)
Greater than $144.49.