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2 answers:
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Answer:
a)
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.
b)
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
c)
And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.
Step-by-step explanation:
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) Part a
Let X the random variable that represent the number of viewers for the American Idol TV of a population, and for this case we know the distribution for X is given by:
Where and
with the values on this case representing millions
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:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Part b
We are interested on this probability :
And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.
Part c
We are interested on this probability :
And in order to find the probabilitiy we can use tables for the normal standard distribution, excel or a calculator.