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The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.
<h3>What does Chebyshev’s Theorem state?</h3>When the distribution is not normal, Chebyshev's Theorem is used. It states that:
- At least 75% of the measures are within 2 standard deviations of the mean.
- At least 89% of the measures are within 3 standard deviations of the mean.
- An in general terms, the percentage of measures within k standard deviations of the mean is given by
.
The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:
- 11.75 - 2 x 1.25 = $9.25.
- 11.75 + 2 x 1.25 = $14.25.
More can be learned about the Chebyshev Theorem at brainly.com/question/25303620
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Answer:
So then the correct answer for this case is:
B) Our student, Z= 1.50; his friend, Z=2.00.
Step-by-step explanation:
Assuming this complete question:
A statistics student wants to compare his final exam score to his friend's final exam score from last year; however, the two exams were scored on different scales. Remembering what he learned about the advantages of Z scores, he asks his friend for the mean and standard deviation of her class on the exam, as well as her final exam score. Here is the information:
Our student: Final exam score = 85; Class: M = 70; SD = 10.
His friend: Final exam score = 45; Class: M = 35; SD = 5.
The Z score for the student and his friend are:
A) Our student, Z= -1.07; his friend, Z= -1.14.
B) Our student, Z= 1.50; his friend, Z=2.00.
C) Our student, Z= 1.07; his friend, Z= -1.14.
D) Our student, Z= 1.07; his friend, Z= 1.50
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
Let X the random variable that represent the scores for our student, and for this case we know that:
The z score is given by:
If we use this we got:
Let Y the random variable that represent the scores for his friend, and for this case we know that:
The z score is given by:
If we use this we got:
So then the correct answer for this case is:
B) Our student, Z= 1.50; his friend, Z=2.00.