Complete question;
The distribution of lengths of salmon from a certain river is approximately normal with a standard deviation of 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution? 26 inches A 28 inches B 30 inches C 33 inches D 34 inches
Option B is correct. The value that is closest to the mean of the distribution is 30inches.
The formula for calculating the z-score is expressed as:
[tex]z=\frac{ x-\mu}{\sigma}[/tex]
Given the following parameters
[tex]\sigma = 3.5\\x = 26in[/tex]
If 10 percent of salmon are longer than 30 inches, then:
Using the z table to get the value corresponding to the mean area 0.1.
Substitute the resulting parameters into the formula to get the mean of the distribution.
[tex]z=\frac{x-\mu}{\sigma}\\-1.285=\frac{26-\mu}{3.5}\\-1.285 \times 3.5 = 26 - \mu\\ -4.4975 = 26 - \mu\\\mu = 26 + 4.4975\\\mu = 30.4975\\\mu \approx 30in[/tex]
Hence the value that is closest to the mean of the distribution is 30inches.
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