Question

you have observed that the average size of a particular goldfish is 1.5 inches long. the standard deviation of the size of the goldfish is 0.25 inches. approximately what is the size of a goldfish such that only 16 percent of the goldfish are smaller from such size

Answer 1

The 16 percent of the goldfish are smaller from 1.25 inches.

Explanation:

Let X denote the size of a particular goldfish.

It is provided that the mean size is, μ = 1.5 inches and standard deviation of the size is, σ = 0.25 inches.

Assume that X is normally distributed.

Compute the size of a goldfish such that only 16 percent of the goldfish are smaller from such size as follows:

P (X < x) = 0.16

⇒ P (Z < z) = 0.16

The z-value for such a probability is:

z = -0.99

*Use a z-table.

Compute the value of x as follows:

`z=(x-\mu)/(\sigma)\\\\-0.99=(x-1.5)/(0.25)\\\\x=1.5-(0.99* 0.25)\\\\x=1.2525\\\\x\approx 1.25`

Thus, the 16 percent of the goldfish are smaller from 1.25 inches.