Question

1. The weight of brain of an animal follows normal distribution with mean 100g and variance 16.
   1. What is the probability that a randomly chosen animal has a brain weigh more than 104g?
   2. Take a sample of 25 animals. What is the probability that the average brain weight of this sample is more than 104g?

Answer 1

Mean = = 100

Variance = = 16

Standard deviation = = 4

a) We have to find  the probability that a randomly chosen animal has a brain weigh more than 104g.

That is we have to find P( X > 104)

For finding this probability we have to find z score.

That is we have to find P(Z > 1)

P(Z > 1) = 1 - P(Z < 1 ) = 1 - 0.8413 = 0.1587 ( Using z table)

b)

Sample size = n = 25

We have to find P( > 104)

For finding this probability we have to find z score.

That is we have to find P(Z > 5)

P(Z > 5) = 1 - P(Z < 5) = 1 - 1 = 0.0000