Write each power of ten in standard notation. 10‐³
1 answer:
9514 1404 393
Answer:
0.001
Step-by-step explanation:
In our base-10 place-value number system, the "places" correspond to powers of 10. Those powers start at 0 in the "ones place", and increase by 1 for each place to the left. That is, the 10s place digits have a place value of 10^1, the 100s place digits have a place value of 10^2 and so on.
The place values to the right of the decimal point work the same way. For each place to the right, the exponent decreases by 1. The tenths place (0.1) digits have a place value of 10^-1, the hundredths place (0.01) digits have a place value of 10^-2, and the thousandths place (0.001) digits have a place value of 10^-3.
10^-3 = 0.001
_____
<em>Additional comment</em>
Some places, 10^-3 <em>is</em> standard notation. That is, what is defined as "standard" varies around the world.
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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.