Answer:
We can calculate the z score given by:
So for this case 14.6 is a value 1 deviation above the mean
We know that within 1 deviation from the mean we have 68% of the data, and on the tails we will have 100-68 = 32% and 16% on each tail, so then we can conclude that:
Step-by-step explanation:
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".
Let X the random variable who represent the lifespans of meerkats.
From the problem we have the mean and the standard deviation for the random variable X.
So we can assume
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
And we want the following probability:
We can calculate the z score given by:
So for this case 14.6 is a value 1 deviation above the mean
We know that within 1 deviation from the mean we have 68% of the data, and on the tails we will have 100-68 = 32% and 16% on each tail, so then we can conclude that: