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?
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.
are you sure
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.