One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in an automobile. The steel is cut with a diamond saw and requires the resulting parts to be within ±0.005 inch of the length specified by the automobile company. The data in the file Steel comes from a sample of 100 steel parts. The measurement reported is the difference in inches between the actual length of the steel part, as measured by a laser measurement device, and the specified length of the steel part. For example, the first value, 0.002, represents a steel part that is 0.002 inch shorter than the specified length.

a. Construct a percentage histogram.
b. Is the steel mill doing a good job in meeting the requirements set by the automobile company? Explain.

nevermind above question, this question please:

Suppose there are three balls in a box. On one of the balls is the number 1, on another is the
number 2, and on the third is the number 3. You select two balls at random and without
replacement from the box and note the two numbers observed. The sample space S consists of
the three equally likely outcomes {(1, 2), (1, 3), (2, 3)}. Let X be the sum of the numbers on the
two balls selected.

Referring to the information above, the variance of X is... (EXPLAIN)

To construct a percentage histogram, we need to follow these steps:

Step 1: Calculate the total number of data points.
In this case, the sample size is given as 100 steel parts.

Step 2: Determine the range of the data.
The range can be found by subtracting the minimum value from the maximum value in the data set. In this case, you would need to find the minimum and maximum values from the "Steel" dataset.

Step 3: Determine the number of intervals (or bins) for the histogram.
The number of intervals is typically determined by taking the square root of the total number of data points and rounding up to the nearest whole number. However, the choice of intervals can vary depending on the context and the desired level of detail. For this question, let's assume we use 10 intervals.

Step 4: Determine the width of each interval.
The width of each interval can be calculated by dividing the range by the number of intervals.

Step 5: Group the data into the appropriate intervals and count the number of data points falling into each interval.
For example, if the first interval starts at -0.01 and ends at -0.005, we would count the number of data points that fall within this range.

Step 6: Calculate the percentage for each interval.
To calculate the percentage, divide the count for each interval by the total number of data points and then multiply by 100.

Step 7: Construct the histogram using the interval widths as the x-axis and the percentages as the y-axis.

Now, let's analyze whether the steel mill is doing a good job in meeting the requirements set by the automobile company:

To assess this, we need to examine the percentage histogram. Look for intervals that have a higher percentage of data points. If most of the data points fall within the ±0.005 inch range specified by the automobile company, it indicates that the steel mill is doing a good job in meeting the requirements. On the other hand, if a significant proportion of the data points fall outside this range, it suggests that the steel mill may not be meeting the requirements.

Additionally, you can also calculate some summary statistics such as mean and standard deviation to get a better understanding of how well the steel mill is doing. A small standard deviation around 0, indicating the measurements are clustered tightly around the specified length, would be desirable.

By analyzing the percentage histogram and considering the summary statistics, you can determine whether the steel mill is meeting the requirements set by the automobile company.