Question

Question 18 Item 18 The distribution of the number of moths captured per night by a certain moth trap is approximately normal with mean 103. If 28 percent of the captures fall below 76 per night, which of the following equations can be used to find σ, the standard deviation of the distribution?

Answer 1

Answer:

Standard deviation 46.3

Step-by-step explanation:

A 28% of the distribution is equivalent to a z score of -0.5828, you can use a z table to find that.

Z score is calculated as follows:

$z = \frac{x-\mu}{\sigma}$

x is the number being evaluated

μ is the mean

σ is the standard deviation

And it is used to calculate how many standard deviations you are from the mean of the sample.

Replacing with the known information you can calculate the standard deviation:

$\sigma=\frac{x-\mu}{z} =\frac{76-103}{-0.5828}= 46.3$