Industrial engineers periodically conduct \"work measurement\" analyses to deter
ID: 3200066 • Letter: I
Question
Industrial engineers periodically conduct "work measurement" analyses to determine the time required to produce a single unit of output. At a large processing plant, the number of total worker-hours required per day to perform a certain task was recorded for 50 days. Measurements in excess of 120 worker-hours include repair activities. The data are shown below: Construct a histogram of the data and comment on any important features that you notice. Construct a box plot for the data. Do you detect any outliers ? Construct the intervals y plusminus S, y plusminus 2S, and y plusminus 3S. Count the number of observations that fall within each interval and find the corresponding proportions. Compare the results to the empirical rule and comment on the results.Explanation / Answer
1.
From the above histogram we find that there is a skewness at right side, the distribution is positively skewed. Here the mean is greater than the value of median.
2.
The above boxplot suggests that there is an outlier and it is the observation 165.
3.
y = 118.1, S = 15.8
y ± S = 118.1 – 15.8 , 118.1 + 15.8 = 102.3 and 133.9 in this interval we find 33 values. The corresponding proportion is 66% (33/50). Empirical rule says that 68% of the data falls in this interval.
y ±2S = 118.1 – 2*15.8 , 118.1 + 2*15.8 = 86.5 and 149.7 in this interval we find 49 values. The corresponding proportion is 98% (49/50). Empirical rule says that 95% of the data falls in this interval.
y ±3S = 118.1 – 3*15.8 , 118.1 + 3*15.8 = 70.7 and 165.5 in this interval we find 50 values. The corresponding proportion is 100% (50/50). Empirical rule says that 99.7% of the data falls in this interval.