Coefficient x^2 in the expansion of (2+x)^5
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Part A
See the attached image to see how to form the double stem-and-leaf plot. Each leaf represents an individual data value. Specifically it is the year number (right-most single digit only). The stem is the rest of the year. The stem and leaf together combine to form the whole year.
For instance, the stem of 196 combined with the leaf of 4 represents the year 1964. This is shown on the image attachment.
The leaf of '4', that is attached to the stem of 196, will go under the "did not reach the summit" column to indicate there was a failed attempt by someone born in 1964. In contrast, there is a successful attempt by someone born in 1973 for instance. So well write '3' next to the 197 in the "reached the summit" column. The rest of the values are sorted in this way. Again see the attached to get a good idea of what is going on.
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Part B
The shape of the distribution for those who reached the summit is fairly symmetrical. The center is around the decade of the 1960s or so. On either side of this center lays values that are fairly equal number. In other words, on the left side is the same amount as the right side. Imagine that the distribution has been tipped to rotate 90 degrees.
In contrast, the distribution for the people who didn't reach the summit is skewed to the left. The majority of the climbers who didn't reach the summit are clustered in the range of 1970 to 1990 or around there. The outliers earlier in the century (eg: 1939) pull the distribution to the left to give it a longer tail. This is why the distibution is skewed to the left.
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Part C
Although the first two attempts ended in failure (1939, 1945), the next three were successful. The status of success or failure would then alternate heavily favoring the success column. Its mainly successes until we reach about 1970 is when the failures start to pile up. So in general there's mainly success at first (ignoring 1939 and 1945) that leads to failure later on. The cause of this swap isn't stated, but it's curious why this is.
See the attached image to see how to form the double stem-and-leaf plot. Each leaf represents an individual data value. Specifically it is the year number (right-most single digit only). The stem is the rest of the year. The stem and leaf together combine to form the whole year.
For instance, the stem of 196 combined with the leaf of 4 represents the year 1964. This is shown on the image attachment.
The leaf of '4', that is attached to the stem of 196, will go under the "did not reach the summit" column to indicate there was a failed attempt by someone born in 1964. In contrast, there is a successful attempt by someone born in 1973 for instance. So well write '3' next to the 197 in the "reached the summit" column. The rest of the values are sorted in this way. Again see the attached to get a good idea of what is going on.
=========================================
Part B
The shape of the distribution for those who reached the summit is fairly symmetrical. The center is around the decade of the 1960s or so. On either side of this center lays values that are fairly equal number. In other words, on the left side is the same amount as the right side. Imagine that the distribution has been tipped to rotate 90 degrees.
In contrast, the distribution for the people who didn't reach the summit is skewed to the left. The majority of the climbers who didn't reach the summit are clustered in the range of 1970 to 1990 or around there. The outliers earlier in the century (eg: 1939) pull the distribution to the left to give it a longer tail. This is why the distibution is skewed to the left.
=========================================
Part C
Although the first two attempts ended in failure (1939, 1945), the next three were successful. The status of success or failure would then alternate heavily favoring the success column. Its mainly successes until we reach about 1970 is when the failures start to pile up. So in general there's mainly success at first (ignoring 1939 and 1945) that leads to failure later on. The cause of this swap isn't stated, but it's curious why this is.