In an attempt to predict future performance on an assembly line, the time to complete assembly of an engine part was investigated. 100 parts were carefully timed, and the time to complete their assembly was recorded. The times, recorded in seconds, were approximately normally distributed: N(14.2, 0.3) . For your calculations, use two decimal places. You can round the second decimal place. For example, 74.8862 can be rounded to 74.89.

In one to two paragraphs, and in your own words, describe what is meant by standard deviation. Note: Do not provide a mathematical explanation. Rather, explain in words what the standard deviation is. You can include numbers if you need them to help with your discussion, but do not show the actual formula for SD. This question is worth up to 3 points. You will be given full points based on your ability to convince the grader that you do indeed understand the concept of SD. Note: You may be asked to do this again on one of your exams.

The line manager will be satisfied as long as parts are completed in less than 14.85 seconds. What percentage of parts do you predict will be completed in this amount of time? Hint: Remember that R's pnorm() function gives the area under the density curve.

One part took 13.89 seconds. What percentile does this correspond to?

How much time would it take to complete a part that is at exactly the 10th percentile?

What percentage of parts do you predict will be completed between 14.0 and 14.4 seconds?

What percentage of parts are made in a time with a z-score of greater than -1?

What percentage of parts are made in a time with a z-score of less than +1.5?