Use the Normal model N(98,15) for the IQs of sample participants. What IQ represents the 17th percentile? Use the appropriate
1 answer:
Answer:
=NORM.INV(0.17,98,15)
Step-by-step explanation:
Consider X represents the IQs of sample participants.
Then X follows the Normal Distribution with mean 98 and standard deviation 15.
That is,
The probability value is 17th percentile (that is 0.17)
To find the value of X using Excel, the<em> Inverse Normal Distribution </em>is used.
The Excel function =NORM.INV(0.22,105,17) is used to find the IQs of sample participants.
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Answer:
a) A z-score of 2.49 means that your grade was 2.49 standard deviations above the mean of all grades.
b) 1.39% of the class scored lower than your friend.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
You got a score of 2.49 on an exam.
(a) Write a sentence explaining what that means
A z-score of 2.49 means that your grade was 2.49 standard deviations above the mean of all grades.
(b) Your friend got a z-score of negative 2−2. If the grades satisfy the Nearly Normal Condition, about what percent of the class scored lower than your friend?
This percentage is the pvalue of
So 0.0139 = 1.39% of the class scored lower than your friend.
For this case we have:
Note:<em> Milliliter is a unit of volume. It is not possible to convert distance units into volume units. </em>
We must convert the length 0.13 meters to millimeters.
By definition, 1 meter equals 1000 millimeters. That is to say:
Then, applying the rule of three we have:
1m ------------> 1000mm
0.13m --------> x
Where x represents the length of the marker in millimeters.
Resolving:
Thus, the marker measures 130 millimeters long
Answer:
130 millimeters