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?
Use z-scores.
Formula:
z = (x - mean)/sd
Find two z-scores:
z = (120 - 160)/20
z = (170 - 160)/20
Once you have the two scores, find the probability using a z-table. Remember that the question is asking 120 or less or 170 or more.
Hope this will help get you started.
Thanks. For the z scores I have:
z = (120 - 160)/20 = -40/20=-2
z = (170 - 160)/20 = 10/20= 0.5
and the z table for 2 -(area between Mean and z) 0.47725, area beyond: 0.02275
For 0.5: 0.19146 and area beyond: 0.30854
What do I do after that, and which # I use? What is the probability?
Hint:
You don't want the probability from mean to z. Remember the problem is asking "120 or less" or "170 or more" for the probability. You use those values. Once you have those values, add them together for the total probability.
2.5
To find the probability of selecting someone who weighs 120 or less or 170 or more pounds, we need to convert these values into standardized z-scores using the formula:
z = (x - μ) / σ
where x is the individual value, μ is the mean, and σ is the standard deviation.
For 120 pounds:
z1 = (120 - 160) / 20 = -2
For 170 pounds:
z2 = (170 - 160) / 20 = 0.5
To find the probability associated with each z-score, we can refer to the standard normal distribution table or use statistical software. Using a standard normal distribution table, we can find the probabilities associated with these z-scores:
For z1 = -2, the probability is P(z ≤ -2) = 0.0228 (approximately)
For z2 = 0.5, the probability is P(z ≥ 0.5) = 0.3085 (approximately)
Now, to find the probability of selecting someone who weighs 120 or less or 170 or more pounds, we need to add these two probabilities:
P(120 or less or 170 or more) = P(z ≤ -2) + P(z ≥ 0.5)
= 0.0228 + 0.3085
= 0.3313 (approximately)
Therefore, the probability of selecting someone who weighs 120 or less or 170 or more pounds is approximately 0.3313, or 33.13%.