Use the empirical rule to answer the problems in this question. Do not use R's function to answer any of these questions. Let's continue with the same assembly line analysis. Data from the manufacturing of a yet another engine part (this one larger) was approximately normally distributed in minutes: N(17.2, 1.8)

pnorm()

One item took 15.4 minutes. What percentile does this correspond to?

What percentage of items took between 17.2 and 22.6 to manufacture?

What percentage of items were made in less than 19 minutes?

One item was manufactured with a z-score of -1. How many minutes did it take to make

this item?

Do not use the empirical rule for this problem. Instead, use R for a precise calculation.

One item was in the 38th percentile. What time does that correspond to? Hint: There is an R function that will give you this exact piece of information. That is, it converts the area under the normal density curve back into a z-score.