Question

In a cooking contest, the mean score for taste was 20, with a standard deviation of 28. One of the contestants received a score of 14. Convert this score to a z-score and determine if it is "usual" or "unusual." Which of the following options is correct? a) z = -2.14; unusual b) z = 2.14; unusual c) z = 0.56; usual d) z = -0.56; usual

Answer 1

To solve this problem, we need to first calculate the z-score, and then determine whether the score is "usual" or "unusual".

Step 1: Calculate the z-score
The z-score is a measurement of how many standard deviations an element is from the mean. The formula to calculate the z-score is:

z = (X - μ) / σ

Where:
X = the element or the score that we're looking at, which in this case is 14
μ = the mean, which is 20
σ = the standard deviation, which is 28

Substituting these values into the formula we get:

z = (14 - 20) / 28
=> z = -6 / 28
=> z = -0.21428571428571427

Step 2: Determine if the score is "usual" or "unusual"
Generally in a normal distribution, a "usual" z-score falls within the range of -2 and +2 standard deviations from the mean, anything beyond this is considered "unusual".

In our case, the z score is -0.21428571428571427 which falls within the range of -2 and +2 hence we can say it's "usual".

From the choices given, none of the options provided are correct as per our calculations.