Question

According to one study, brain weights of men are normally distributed with a mean of 1.50kg and a standard deviation of 0.14kg.

1) determine the percentage of all samples of three men that have mean brain weights withon 0.1kg of the population mean brain weight of 1.50kg.

2) determine the percentage of all samples of twelve men that have mean brain weights within 0.1kg of the population mean brain weight of 1.50kg

Answer 1

Let X denote the brain weight for men.

Using Central Limit theorem, we know,

1)

Now,

So, reuqired percentage = 78.502%

2)

Now,

So, reuqired percentage = 98.648%