Students from Texas, New York, Washington, Florida, and Utah identified their area of concentration at various universities. The
results are listed in the table.
One of these students is selected at random. What is the probability that the student is from the state of Washington under the condition that the student studies history?
Enter a number in the box.
One of these students is selected at random. What is the probability that the student is from the state of Washington under the condition that the student studies history?
Enter a number in the box.
2 answers:
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Answer:
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".
Solution to the problem
Let X the random variable that represent the lifetime for a TV of a population, and for this case we know the distribution for X is given by:
Where and
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 like this:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.