The slope of the line below is 1.write the point-slope equation for the line using the coordinates of the labeled point.
1 answer:
Answer:
or
Step-by-step explanation:
We know that the slope of the line is 1, so we can write it in terms of any two points belonging to the line, as per the difinition of slope:
We can use instead of any general point (x,y) on the line, and for
the point we are interested in: (11,4)
That way the slope can be written as:
Next we can solve for y if this format is the one your instructor prefers:
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<h3>Answer: </h3>
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Explanation:
The data set for Ali is
8.3, 5.9, 8.3, 8.9, 7.7, 7.2, 8.1, 9.1, 9.8, 5.8,
8.3, 4.7, 7.0, 6.5, 6.5, 8.4, 8.8, 8.1, 8.9, 9.9
which when on a single line looks like this
8.3, 5.9, 8.3, 8.9, 7.7, 7.2, 8.1, 9.1, 9.8, 5.8, 8.3, 4.7, 7.0, 6.5, 6.5, 8.4, 8.8, 8.1, 8.9, 9.9
Let's sort the values from smallest to largest
4.7, 5.8, 5.9, 6.5, 6.5, 7.0, 7.2, 7.7, 8.1, 8.1, 8.3, 8.3, 8.3, 8.4, 8.8, 8.9, 8.9, 9.1, 9.8, 9.9
Now lets break the data up into separate rows such that each time we get to a new units value, we move to another row
4.7
5.8, 5.9
6.5, 6.5
7.0, 7.2, 7.7
8.1, 8.1, 8.3, 8.3, 8.3, 8.4, 8.8, 8.9, 8.9
9.1, 9.8, 9.9
We have these stems: 4, 5, 6, 7, 8, 9 which represent the units digit of the values. The leaf values are the tenths decimal place.
For example, a number like 4.7 has a stem of 4 and leaf of 7 (as indicated by the key below)
This is what the stem-and-leaf plot looks like for Ali's data only
The stem-and-leaf plot condenses things by tossing out repeated elements. Instead of writing 8.1, 8.1, 8.3 for instance, we can just write a stem of 8 and then list the individual leaves 1, 1 and 3. We save ourselves from having to write two more copies of '8'
Through similar steps, this is what the stem-and-leaf plot looks like for Kumar's data set only
Kumar doesn't have any leaves for the stem 6, so we will have that section blank. It's important to have this stem so it aligns with Ali's stem plot.
Notice that both stem plots involve the same exact set of stems (4 through 9 inclusive).
What we can do is combine those two plots into one single diagram like this
Then the last thing to do is reverse each set of leaves for Ali (handle each row separately). The reason for this is so that each row of leaf values increases as you further move away from the stem. This is simply a style choice. This is somewhat similar to a number line, except negative values aren't involved here.
This is what the final answer would look like
The fact that Ali is on the left side vs Kumar on the right, doesn't really matter. We could swap the two positions and end up with the same basic table. I placed Ali on the left because her data set is on the top row of the original table given.
The thing you need to watch out for is that joining the stem and leaf for Ali means you'll have to read from right to left (as opposed to left to right). Always start with the stem. That's one potential drawback to a back-to-back stem-and-leaf plot. The advantage is that it helps us compare the two data sets fairly quickly.
Answer:
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly
This probability is the pvalue of Z when X = 1600 + 300 = 1900 subtracted by the pvalue of Z when X = 1600 - 300 = 1300. So
X = 1900
By the Central Limit Theorem
has a pvalue of 0.9535.
X = 1300
has a pvalue of 0.0465.
0.9535 - 0.0465 = 0.907.
The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.