Question

Given a mean of 61.2 and a standard deviation of 21.4, within how many standard deviations of the mean do the values 45, 78, 62, 90, and 31 fall?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find how many standard deviations a value is from the mean, you can use the formula:

z = (x - mean) / standard deviation

where z is the number of standard deviations from the mean, x is the value, mean is the mean, and standard deviation is the standard deviation.

For the values 45, 78, 62, 90, and 31:

z_1 = (45 - 61.2) / 21.4
z_2 = (78 - 61.2) / 21.4
z_3 = (62 - 61.2) / 21.4
z_4 = (90 - 61.2) / 21.4
z_5 = (31 - 61.2) / 21.4

Calculating these values, we get:

z_1 ≈ -0.756
z_2 ≈ 0.785
z_3 ≈ 0.037
z_4 ≈ 1.344
z_5 ≈ -1.409

So the values 45, 78, 62, 90, and 31 fall within approximately -1.41, -0.76, 0.04, 0.79, and 1.34 standard deviations of the mean, respectively.

Answer 2

are you sure

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the previous incorrect response. Let's recalculate the number of standard deviations from the mean for the given values.

z_1 = (45 - 61.2) / 21.4 ≈ -0.756
z_2 = (78 - 61.2) / 21.4 ≈ 0.785
z_3 = (62 - 61.2) / 21.4 ≈ 0.037
z_4 = (90 - 61.2) / 21.4 ≈ 1.345
z_5 = (31 - 61.2) / 21.4 ≈ -1.415

So the correct results are:
- Value 45 is approximately -0.756 standard deviations from the mean.
- Value 78 is approximately 0.785 standard deviations from the mean.
- Value 62 is approximately 0.037 standard deviations from the mean.
- Value 90 is approximately 1.345 standard deviations from the mean.
- Value 31 is approximately -1.415 standard deviations from the mean.