Question

The mean weight of 500 college students is 70 kg and the standard deviation is 3 kg. Assuming that the weight is normally distributed, determine what percentage of students weigh over 75 kg

Answer 1

Answer: 4.75%.

Step-by-step explanation:

Given: The mean weight $(\mu)$ of 500 college students is 70 kg and the standard deviation$(\sigma)$ is 3 kg.

Let X be the number of students weight over 75 kg.

If the weight is normally distributed, then the probability that students weigh over 75 kg:

$P(X>75)=P(\dfrac{X-\mu}{\sigma}>\dfrac{75-70}{3})\\\\=P(z>\dfrac53)\\\\=P(z>1.67)\\\\=1-P(z$

Hence, the  percentage of students weigh over 75 kg = 4.75%.