Question

In a population of Siberian flying squirrels in western Finland, assume that the the number of pups born to each female over her lifetime has mean ?=3.66 and standard deviation ?=2.9598. The distribution of squirrel pups born is non‑normal because it takes only whole, non‑negative values.

Determine the mean number of pups, x¯, such that in 70% of all random samples of such squirrels of size ?=40, the mean number of pups born to females in the sample is less than ?⎯⎯⎯.

Answer 1

Given that,

mean = = 3.66

standard deviation = = 2.9598

n = 40

= 3.66

= / n =2.9598 /40=0.4680

Using standard normal table,

P(Z < z) = 70%

= P(Z < z) = 0.70  

= P(Z <0.52 ) = 0.70

z = 0.52    Using standard normal table,

Using z-score formula  

= z * +   

=0.52 *0.4680+3.66

= 3.90336