One dimension of bird beaks is “depth”—the height of the beak where it arises from the bird's head. During a research study on one island in the Galapagos archipelago, the beak depth of all Medium Ground Finches on the island was found to be normally distributed with mean u = 9.5 millimeters and standard deviation o = 1.0 millimeter.
(a) What is the probability that a randomly selected medium ground finches is at least 10 millimeters?
P ( Z > = 10 ) = 1 - P ( Z < 10 )
Calculating Z = (score - mean ) / standard deviation
= ( 10 - 9.5 ) / 1. 0 = 0.5 / 1. 0= 0.5
P ( Z < 0.5 ) = 0.5 + 0. 1915 = 0.6915
P ( Z > = 10 ) = 1 - P ( Z < 10 )
= 1 - 0.6915
= 0.3085
b) What is the probability that the mean depth x in 10 randomly selected medium ground finches is at least 10 millimeters?
This is an example of T-score;
T- score = ( Given value - mean ) / ( standard deviation/ square root n )
= (10 - 9.5 ) / ( 1.0 / square root 10 )
= 0.5 / ( 1.0 / 3.16)
= 0.5 / 0.316
T- score = 1.582
T -score of 1.582 = 3.078