Complete question;
<em>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</em>
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:
Given the following parameters
If 10 percent of salmon are longer than 30 inches, then:
- P(x>30) = 0.1
Using the z table to get the value corresponding to the mean area 0.1.
- The required z-score will be -1.285
Substitute the resulting parameters into the formula to get the mean of the distribution.
Hence the value that is closest to the mean of the distribution is 30inches.
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