Answer:
And then the probability that will be farther away from the mean than + 3 standard deviations is just
1-0.9973= 0.0027
And the number of cases would be 1000*0.0027=2.7 or approximatley 3 cases. And the bes option is : a.About 3
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
And then the probability that will be farther away from the mean than + 3 standard deviations is just
1-0.9973= 0.0027
And the number of cases would be 1000*0.0027=2.7 or approximatley 3 cases. And the bes option is : a.About 3