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?
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To calculate the probability of selecting someone who weighs 120 or less or 170 or more pounds, we need to use the normal distribution formula.
First, let's find the z-scores for each weight value using the formula:
z-score = (x - μ) / σ
where x is the value we want to calculate the probability for (120 and 170), μ is the mean (average) weight, and σ is the standard deviation.
For 120 pounds:
z-score = (120 - 160) / 20 = (-40) / 20 = -2
For 170 pounds:
z-score = (170 - 160) / 20 = 10 / 20 = 0.5
Now, we need to find the area under the normal curve for each z-score.
Using a z-table or a statistical calculator, we can find the probabilities associated with these z-scores.
For z = -2, the corresponding probability is 0.0228 (or 2.28%).
For z = 0.5, the corresponding probability is 0.6915 (or 69.15%).
Since we are interested in the probability of selecting someone who weighs 120 or less or 170 or more pounds, we need to sum the probabilities for these two cases.
Probability = P(z ≤ -2) + P(z ≥ 0.5)
= 0.0228 + (1 - 0.6915)
= 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%).