Question

If

x_max = 150 and
x_min = 90 and the population is normal, one could estimate
σ to be ___.

Answer 1

To estimate the standard deviation of a normal population given minimum and maximum values, we can use the formula (x_max - x_min) / (2 * k), where k is the number of standard deviations away from the mean. Plugging in the given values, we find that the estimated standard deviation is 15.

Step-by-step explanation:

To estimate the standard deviation (σ) of a normal population when x_max is given as 150 and x_min is given as 90, we can use the formula:

σ ≈ (x_max - x_min) / (2 * k)

where k is the number of standard deviations away from the mean. Since the population is normal, we can assume that about 95% of the data falls within 2 standard deviations of the mean. Therefore, k = 2.

Plugging in the values, we get:

σ ≈ (150 - 90) / (2 * 2) = 15

So, the estimated standard deviation (σ) is 15.