The mean weight of a group of boys is 165 lb, with a standard deviation of 20 lb. If the weights are normally distributed, find the probability that one of the boys picked at random from the group weighs between 150 and 195 lb. Round your answer to four decimal places.
A)0.4332
B)0.2734
C)0.1598
D)0.7066
E)0.2934

Question

The mean weight of a group of boys is 165 lb, with a standard deviation of 20 lb. If the weights are normally distributed, find the probability that one of the boys picked at random from the group weighs between 150 and 195 lb. Round your answer to four decimal places. ​
A)0.4332
B)0.2734
C)0.1598
D)0.7066
E)0.2934

Quizplus · Accepted Answer

We need to find the probability that a randomly selected boy weighs between 150 and 195 lb. We can calculate the z-scores for these weights as follows:

z1 = (150 - 165) / 20 = -0.75
z2 = (195 - 165) / 20 = 1.5

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:

P(-0.75 < Z < 1.5) = 0.7066

Therefore, the probability that a randomly selected boy weighs between 150 and 195 lb is 0.7066, which corresponds to choice D.

The Mean Weight of a Group of Boys Is 165