Seattle, Washington is known for being very rainy. One day last month, 8 inches of rain fell in 1 1/2 hours. What is the rate of
2 answers:
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Answer:
a)
b)
c)
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 415.8.
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 SAT scores 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 using the complement rule and with the normal standard table or excel:
Part b
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 with this difference:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Part c
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 415.8.
To find the answer set up an equation:
Using this set up we can cross our units of pages since they are on opposite side of the proportion, leaving us with the desired units of hours.
Then divide 400 by 65 which will give us our answer: 6.15 or about 6 hours for Jamie to finish her reading.
Using this set up we can cross our units of pages since they are on opposite side of the proportion, leaving us with the desired units of hours.
Then divide 400 by 65 which will give us our answer: 6.15 or about 6 hours for Jamie to finish her reading.