Answer to Question #152066 in Statistics and Probability for shn

Question

Weights. If the weights of 600 students are normally distributed with a mean of 50 kilograms and a variance of 16 kilograms
a. Determine the percentage of students with weights lower than 55 kilograms.
b. How many students have weights exceeding 52 kilograms?

Answer 1

$\mu=50$

$\sigma=16$

$n=600$

a) $P(X<55)=P(Z<\frac{55-\mu}{\sigma})=P(Z<\frac{55-50}{16})=P(Z<0.3125)=0.6217$

wich is 62.17%

b) $P(X>52)=P(Z>\frac{52-50}{16})=P(Z>0.125)=1-P(Z<0.125)=$

$=1-0.5478=0.4522$

$600\cdot0.4522=271$

Answer:

a) 62.17% of students with weights lower than 55 kilograms

b) 271 students have weights exceeding 52 kilograms