Question

Let's try putting the CLT (Central Limit Theorem) to practice. In a study of bumblebee bats, one of the world’s smallest mammals, the weights have a mean of 2.0 grams and a standard deviation of 0.25 gram.

a) Find the probability that a randomly selected bat from the study weights more than 2.3 grams.

b) A random sample of 7 bumblebee bats is selected from the study. Find the probability that the mean weight of the sample is more than 2.3 grams.

c) A random sample of 40 bumblebee bats is selected from the study. Find the probability that the mean weight of the sample is more than 2.3 grams.

Answer 1

Part a)

P ( X > 2.3 ) = 1 - P ( X < 2.3 )
Standardizing the value

Z = ( 2.3 - 2 ) / 0.25
Z = 1.2

P ( Z > 1.2 )
P ( X > 2.3 ) = 1 - P ( Z < 1.2 )
P ( X > 2.3 ) = 1 - 0.8849
P ( X > 2.3 ) = 0.1151

Part b)

P ( X > 2.3 ) = 1 - P ( X < 2.3 )
Standardizing the value


Z = 3.17

P ( Z > 3.17 )
P ( X > 2.3 ) = 1 - P ( Z < 3.17 )
P ( X > 2.3 ) = 1 - 0.9993
P ( X > 2.3 ) = 0.0007

Part c)

P ( X > 2.3 ) = 1 - P ( X < 2.3 )
Standardizing the value


Z = 7.59

P ( Z > 7.59 )
P ( X > 2.3 ) = 1 - P ( Z < 7.59 )
P ( X > 2.3 ) = 1 - 1
P ( X > 2.3 ) = 0