A computer programmer creates a probability distribution table when working with generated values appearing in a program. She determines that the mean of the probability distribution is 65.1 in the standard deviation is 9.7. If the value 84.9. Would it be considered usual or unusual?
To determine whether the value 84.9 would be considered usual or unusual, we need to compare it to the probability distribution table and see how many standard deviations away from the mean it is.
To do this, we can calculate the z-score, which tells us the number of standard deviations a value is away from the mean. The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
x is the value we want to calculate the z-score for (84.9 in this case),
μ is the mean of the probability distribution (65.1), and
σ is the standard deviation of the probability distribution (9.7).
Plugging in these values:
z = (84.9 - 65.1) / 9.7
z = 2.04
The z-score of 2.04 indicates that the value 84.9 is 2.04 standard deviations above the mean.
In general, a z-score of:
- Less than 1.96 (or greater than -1.96) is considered usual or within a normal range (about 95% of data falls within this range in a normal distribution).
- Greater than 1.96 (or less than -1.96) is considered unusual or outside of the normal range (about 5% of data falls outside this range in a normal distribution).
Since the z-score of 2.04 is greater than 1.96, we can conclude that the value 84.9 would be considered unusual or outside of the normal range based on the given probability distribution.