Final answer:
The correct statement based on the given information is b: on average the number of cat naps deviate from the mean by 4 naps. A z-score calculation shows that a cat which takes 10 naps has a z-score of -0.5, not +0.5 as suggested in choice a.
Step-by-step explanation:
To answer the question, we use the concept of the z-score, which measures the number of standard deviations a particular value is from the mean of a data set. The formula to calculate a z-score is:
Z = (X - μ) / σ
where X is the value in question, μ (mu) is the mean, and σ (sigma) is the standard deviation.
Given that the average number of naps per day for a cat is 12 (mean) and the standard deviation is 4 naps, if a cat naps 10 times per day, the z-score can be found as follows:
Z = (10 - 12) / 4
Z = -2 / 4
Z = -0.5
The correct statement based on this calculation is:
b. on average the number of cat naps deviate from the mean by 4 naps
The z-score of -0.5 for a cat that naps 10 times indicates it naps 0.5 standard deviations below the mean, not above as statement a incorrectly suggests. Statement c cannot be directly inferred from the information given since the median is not necessarily equal to the mean, especially without knowing the distribution's shape. Therefore, only one of the statements provided is correct, and it is b.