The scores of eighth-grade students in a math test are normally distributed with a mean of 57.5 and a standard deviation of 6.5.
2 answers:
Answer:
Step-by-step explanation:
Empirical Rule-
- 68% of data falls within the one standard deviation from the mean.
- 95% fall within two standard deviations from the mean.
- 99.7% fall within three standard deviations from the mean.
Here, the normal distribution has the mean as 57.5 and standard deviation as 6.5
So the 68% of the score will lie between,
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Answer:
3. The mean will increase more than median, but both will increase.
Step-by-step explanation:
We have been given a dot plot. We are asked to find the true statement, if a new data point at 12 is added to our given dot plot.
Since we know that an large valued outlier affects mean more than median, so mean will increase more than median.
Let us check this using our given information. Our data set before adding 12 is:
1, 2, 2, 2, 3, 4, 4, 4, 5.
We can see that our data set has odd number (9) of data points, so median will be the value of 5th term, that is 3.
Therefore, mean of our data set is 3.
Upon adding a data point at 12, our new data set will be:
1, 2, 2, 2, 3, 4, 4, 4, 5, 12.
Now our data set has 10 terms, so median will be the average of 5th and 6th term.
Therefore, the median of new data set will be 3.5.
Therefore, mean of new data set will be 3.9.
Upon looking at our given statements we can see that 3rd statement is true as mean and median both increased after adding 12 to our data set, but mean increased more that median. Mean and median before adding 12 was 3; but after adding 12 median became 3.5, while mean became 3.9 (which is greater than mean).
Answer:
The original function was transformed by a a horizontal shift to the right in 1 unit, and also a vertical shift upwards of 5 units.
Step-by-step explanation:
Recall the four very important rules regarding translations (shifts) of the graph of functions:
1) In order to shift the graph of a function vertically c units upwards, we must transform f (x) by adding c to it.
2) In order to shift the graph of a function vertically c units downwards, we must transform f (x) by subtracting c from it.
3) In order to shift the graph of a function horizontally c units to the right, we must transform the variable x by subtracting c from x.
4) In order to shift the graph of a function horizontally c units to the left, we must transform the variable x by adding c to x.
We notice that in our case, The original function has been transformed by "subtracting 1 unit from x", and by adding 5 units to the full function. Therefore we are in the presence of a horizontal shift to the right in 1 unit (as explained in rule 3), and also a vertical shift upwards of 5 units (as explained in rule 1).