Question

in a cooking contest, the mean score for taste was 20, with a standard deviation of 2.8. one of the contestants received a score of 14. convert this score to a z score and tell if it is \usual\ or \unusual.\ (1 point) -2.14; unusual 2.14; unusual 0.56; usual -0.56; usual

Explanation:

Step1: Recall the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

Given \(\mu = 20\), \(\sigma=2.8\), and \(x = 14\). Then \(z=\frac{14 - 20}{2.8}=\frac{-6}{2.8}\approx - 2.14\).

Step3: Determine if the z - score is usual or unusual

A z - score is considered unusual if \(|z|\gt2\). Since \(|z| = |-2.14|=2.14\gt2\).

Answer:

-2.14; unusual