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?

Question

Mathematics

Madisyn Short

29 April, 18:34

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?

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Answers (1)

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Ibrahim Hall · 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