Solution
- The number of possible outcomes in the sample space is simply gotten by multiplying out all the events together.
- There are 3 possible days: Tuesday, Wednesday, or Thursday. Thus, there are 3 possible outcomes.
- There are 3 possible times: 3PM, 4PM, or 5PM. Thus, there are 3 possible outcomes again.
- There are also 9 possible classrooms available meaning another 9 possible outcomes.
- Thus, the total possible outcomes in the sample space is
Answer:
a)
b)
c)
d)
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".
Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
We select a random sample of n=36. And from the central limit theorem we know that the distribution for the sample is given by:
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:
Part b
For this case we want this probability:
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.
Part c
If we apply this formula to our probability we got this:
Part d
For this case we want this probability:
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.