Question

the lengths of adult blue whales are normally distributed with a mean of 30 meters and a standard deviation of 6 meters. what is the probability that a randomly selected adult blue whale would have the length that differs from the population mean by less than 3 meters?

Answer 1

mean = 30

sd = 6

we need to find the probability that an adult blue whale whale would have length that differs from population mean by less than 3 mts. i.e. length can be between 27 to 33

P( 27 < x < 33)

P (−0.50 < Z < 0.50 ) = P ( Z < 0.50 ) − P (Z < −0.50 )

P ( Z<0.50 )=0.6915 (from standard normal table)

P ( Z<−0.50) = 1−P ( Z < 0.5 ) = 1−0.6915 = 0.3085

P (−0.50 < Z < 0.50 ) = P ( Z < 0.50 ) − P (Z < −0.50 ) = 0.6915 - 0.3085 = 0.383

ANS: Probability that an adult blue whale whale would have length that differs from population mean by less than 3 mts = 0.383