Question

In a study of bumblebee bats, one of the world's smallest mammals, the weights are normally distributed, with a mean of 2.0 grams and a standard deviation of .25 grams.

Find the probability that a bat randomly selected from the study will have a weight between 1.7 and 1.9?

Answer 1

Here, μ = 2, σ = 0.25, x1 = 1.7 and x2 = 1.9. We need to compute P(1.7<= X <= 1.9).

The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (1.7 - 2)/0.25 = -1.2
z2 = (1.9 - 2)/0.25 = -0.4

Therefore, we get
P(1.7 <= X <= 1.9) = P((1.9 - 2)/0.25) <= z <= (1.9 - 2)/0.25)
= P(-1.2 <= z <= -0.4) = P(z <= -0.4) - P(z <= -1.2)
= 0.3446 - 0.1151
= 0.2295