Question

with a mean of 75 and a standard deviation of 10 what percentage is between 65 and 95

Answers

GPT 3.5
To calculate the percentage of values between 65 and 95, we can use the z-score formula:

z = (x - μ) / σ

where:
x = specific value (e.g., 65 or 95)
μ = mean
σ = standard deviation

For the lower value, 65:
z = (65 - 75) / 10 = -1

For the upper value, 95:
z = (95 - 75) / 10 = 2

Now, we can use a standard normal distribution table or calculator to find the percentage of values between -1 and 2.

The table typically provides the percentage of values to the left of a given z-score. Since we are interested in the percentage between -1 and 2, we need to find the proportion to the left of 2 (0.9772) and subtract the proportion to the left of -1 (0.1587):

P(-1 < z < 2) = P(z < 2) - P(z < -1)
P(-1 < z < 2) = 0.9772 - 0.1587 = 0.8185

So, approximately 81.85% of the values are between 65 and 95.

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