Answer to Question #255690 in Statistics and Probability for Pro

Question

The mean weight of 800 college students is 56 kg and the standard deviation is 5 kg. Assuming that the weight is normally distributed, determine how many students weigh: a. Between 60 kg and 70 kg. b. More than 68 kg.

Answer 1

a.

$$P(60<X<70)=P(X<70)-P(X\leq 60)$$

$$=P(Z<\dfrac{70-56}{5})-P(Z\leq \dfrac{60-56}{5})$$

$$=P(Z<2.8)-P(Z\leq 0.8)$$

$$\approx0.9974449-0.7881446\approx 0.209300$$

$$0.209300(800)=167$$

167 students weigh between 60 kg and 70 kg.

b.

$$P(X>68)=1-P(X\leq 68)$$

$$=1-P(Z\leq \dfrac{68-56}{5})=1-P(Z\leq 2.6)$$

$$\approx0.004661$$

$$0.004661(800)=4$$

4 students weigh more than 68 kg.