To solve this problem, we need to find the z-scores corresponding to 25 and 32, and then use the z-score table to find the percentage of data values that are less than -z-25 or greater than z-32.
The z-score formula is given by z = (X - μ) / σ, where X is the data value, μ is the mean, and σ is the standard deviation.
For X = 25:
z-25 = (25 - 28.5) / 3.5 = -1
For X = 32:
z-32 = (32 - 28.5) / 3.5 = 1
Using the z-score table, we find that the percentage of data values that are less than -1 or greater than 1 is approximately 0.6827. However, we need to find the percentage of data values that are less than -1 (less than 25) or greater than 1 (greater than 32).
Since the normal distribution is symmetrical, we can subtract 0.6827 from 1 and divide by 2 to find the percentage that is either less than -1 or greater than 1.
(1 - 0.6827) / 2 = 0.1587
This means that 15.87% of data values in the dataset are expected to be less than 25 or greater than 32.
Therefore, the answer is not listed in the given options.
A dataset that is normally distributed has a mean of 28.5 and a standard deviation of 3.5. What percentage of data values in the dataset are expected to be less than 25 or greater than 32?
A) 5%
B) 68%
C) 32%
D) 95%
1 answer
1 answer