Question

2. Assume that the weights of a teenager were normally distributed with the mean of 63 kg. and a standard deviation of 2.5 kg.

a. What is the probability that their mean weight is greater than 62 kg?

b. If 70 teenagers are randomly selected, what is the probability that the mean weight is greater than 62 kg?

Answer 1

Given that: $\mu=63, \sigma=2.5$

a. $P(\=X>62)=P(Z>\frac{62-63}{2.5})=P(Z>-0.4)=1-P(Z\le-0.4)=1-0.3446=0.6554$

(We found P using z-score table)

b.

$P(\=X>62)=P(Z>\frac{62-63}{2.5/\sqrt{70}})=P(Z>-0.048)=1-P(Z\le-0.048)=1-0.4801=0.5199$