Answer to Question #260344 in Statistics and Probability for wanna

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:

Answer 1

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.

$\mu=56 \\ \sigma= 5$

a.

$P(60<X<70) = P(X<70) -P(X<60) \\ = P(Z < \frac{70-56}{5}) -P(Z < \frac{60-56}{5}) \\ = P(Z< 2.8) -P(Z< 0.8) \\ = 0.9974 -0.7881 \\ = 0.2093 \\ N = 0.2093 \times 800 = 167$

b.

$P(X> 68) = 1 -P(X< 68) \\ = 1 -P(Z< \frac{68 -56}{5}) \\ = 1 -P(Z< 2.4) \\ = 1 -0.9918 \\ = 0.0082 \\ N = 0.0082 \times 800 = 6.56 ≈ 7$