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HACTEHA
2 months ago
6

Question 18 Item 18 The distribution of the number of moths captured per night by a certain moth trap is approximately normal wi

th 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?
Mathematics
1 answer:
Leona [12.6K]2 months ago
4 0

Answer:

The standard deviation is 46.3.

Step-by-step explanation:

A proportion of 28% below a value equates to a z-score of approximately -0.5828, determined by consulting a z-table.

The z-score formula is:

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

Where x is the observed value, μ is the mean, and σ is the standard deviation.

This formula helps measure the distance in standard deviations between x and the mean.

By substituting known values, you can solve for the standard deviation:

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

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