If weight in the general population is normally distributed with an average of 160 and a standard deviation of 20 pounds, what is the probability of selecting someone who weights 120 or less or 170 or more pounds?
To find the probability of selecting someone who weighs 120 or less or 170 or more pounds, we need to calculate the area under the normal distribution curve in those ranges.
First, we need to standardize the values of 120 and 170 using the formula:
z = (x - μ) / σ
where z is the standardized value, x is the given value, μ is the mean, and σ is the standard deviation.
For 120 pounds:
z = (120 - 160) / 20
= -2
For 170 pounds:
z = (170 - 160) / 20
= 0.5
Now, we can use a standard normal distribution table or a calculator to find the probabilities associated with these z-values.
Using a standard normal distribution table, we find that the probability of a z-value of -2 or less is approximately 0.0228 (or 2.28%).
Using the same table, we find that the probability of a z-value of 0.5 or more is approximately 0.3085 (or 30.85%).
Since we want the probability of either event happening (120 or less OR 170 or more), we need to add the probabilities together:
0.0228 + 0.3085 = 0.3313
Therefore, the probability of selecting someone who weighs 120 or less or 170 or more pounds is approximately 0.3313 (or 33.13%).