Answer:
a)
b)
c)
d)
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 measurements.
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
So we need values such that
Part a
We want this probability:
Using the empirical rule probabilities we can do this:
Part b
We want this probability:
Using the empirical rule probabilities we can do this:
Part c
We want this probability:
Using the empirical rule probabilities we can do this:
Part d
We want this probability:
Using the empirical rule probabilities and the complement rule we can do this: