Question

A different species of cockroach has weights that follow a normal distribution with a mean of 50 grams. after measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams. based on this report,what is the approximate standard deviation of the weights for this species of cockroaches?

Answer 1

Given:
μ = 50 g, the mean
Let σ = the standard deviation.

For the random variable x =55 g, the z-score is
z = (55 - 50)/σ

We know that P(x > 55) =0.14 (14%).
From standard tables,
P(x > 55) = 0.14 => z = 0.36  (see the figure below).

Therefore
(55 - 50)/σ = 0.36
5/σ = 0.36
σ = 13.9

Answer: 13.9 grams