What z-score values form the boundaries for the middle 60% of a normal
distribution?
a. z = +0.25 and z = –0.25
b. z = +0.39 and z = –0.39
c. z = +0.52 and z = –0.52
d. z = +0.84 and z = –0.84
How about d?
what was the answer???
To find the z-score values that form the boundaries for the middle 60% of a normal distribution, we need to find the z-scores that correspond to the cutoff points of the middle 60% in the standard normal distribution.
The total area under a standard normal curve is 1, and we want to find the z-scores that correspond to the cutoff points of the middle 60% (which is 60% of 1, or 0.6).
To find the z-score that corresponds to the cutoff point of the middle 60%, we can start by finding the area to the right of this point on the curve. Since the total area under the curve is 1, the area to the right of the cutoff point is (1 - 0.6) / 2 = 0.2 / 2 = 0.1. This means that the area to the left of the cutoff point is also 0.1.
Using a standard normal distribution table or a statistical software, we can find that the z-score that corresponds to an area of 0.1 to the left of it is approximately -1.28.
Therefore, the z-score value that forms the boundary for the left side of the middle 60% is -1.28.
To find the z-score that corresponds to the cutoff point on the right side of the middle 60%, we can subtract the z-score for the left side from 0.6 to get the area to the right of the right cutoff point. The area to the right of the right cutoff point is also 0.1, so we can find the z-score that corresponds to it using the same method as above.
Therefore, the z-score that corresponds to the right boundary is also approximately 1.28.
In conclusion, the z-score values that form the boundaries for the middle 60% of a normal distribution are approximately -1.28 and 1.28.
Therefore, the correct answer is d. z = +0.84 and z = –0.84.
To find the z-scores that form the boundaries for the middle 60% of a normal distribution, we need to find the z-scores that capture 30% on each side of the mean.
The middle 60% of a normal distribution corresponds to the area between the z-scores of -0.5 (30% to the left of the mean) and +0.5 (30% to the right of the mean).
So, the correct answer is c. z = +0.52 and z = –0.52.