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A Manufacturer of Lightbulbs Picks 10 Lightbulbs at Random Each

question 63

Multiple Choice

A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean and range (in hours) of the lifetimes of the 10 lightbulbs are calculated. The results for
12 consecutive days are shown in the table below. Construct an R chart to determine whether
The process is in statistical control. $\begin{array}{c|c|c|c}\text { Day } & \overline{\boldsymbol{x}} & \text { Range } & s \\\hline 1 & 201.1 & 3.4 & 1.2 \\2 & 203.4 & 4.7 & 1.7 \\3 & 200.9 & 3.1 & 0.9 \\4 & 205.6 & 6.2 & 2.3 \\5 & 201.3 & 4.7 & 1.3 \\6 & 200.5 & 3.7 & 1.7 \\7 & 205.8 & 5.8 & 2.1 \\8 & 203.7 & 6.2 & 2.9 \\9 & 199.8 & 2.1 & 0.8 \\10 & 202.7 & 4.4 & 1.6 \\11 & 200.0 & 2.7 & 0.7 \\12 & 204.6 & 7.8 & 3.0\end{array}$
$\text { Control Chart Constants }$
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\bar{x}$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\boldsymbol{s}$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\boldsymbol{R}$
$\begin{array}{ccccccc}\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \\\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \\3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \\4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \\5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \\6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \\7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \\8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \\9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \\10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \\\hline\end{array}$

Definitions:

Present Value

The present worth of a future sum of money or sequence of cash payments, reduced at a particular rate of interest.

An abbreviation for present value, referring to the value today of a future payment or series of payments, adjusted for a specific rate of return.

Discount Rate

This rate, integral to discounted cash flow analysis, is employed for determining the present value of cash flows expected in the forthcoming periods.

Compounding

Compounding in finance refers to the process where an asset's earnings, from either capital gains or interest, are reinvested to generate additional earnings over time.