Chapter PI, Problem 37RE

(a)

To determine

To find out the standard deviation of the assembly time model.

Answer to Problem 37RE

  $0.4296$ .

Explanation of Solution

It is given in the question that a company that markets build it yourselves furniture sells a computer desk that is advertised with the claim “less than an hour to assemble”. The company has learned that only $25\%$ of its customers succeeded in building the desk in under an hour. The mean time was $1.29$ hours. The company assumes that consumer assembly time follows a normal model. Thus, the standard deviation n of the assembly time model will be calculated as first we will find the z -score associated with $0.25$ in the table is as:

  $-0.675$

Then, the standard deviation is as:

  $\begin{array}{l}\sigma =\frac{x-\overline{x}}{z}\\ =\frac{1-1.29}{-0.675}\\ =0.4296\end{array}$

(b)

To determine

To explain what assembly line should the company quote in order that $60\%$ of customers succeed in finishing the desk by then.

Answer to Problem 37RE

  $1.3974$ .

Explanation of Solution

It is given in the question that a company that markets build it yourselves furniture sells a computer desk that is advertised with the claim “less than an hour to assemble”. The company has learned that only $25\%$ of its customers succeeded in building the desk in under an hour. The mean time was $1.29$ hours. Thus, to find the assembly line should the company quote in order that $60\%$ of customers succeed in finishing the desk by then, we need to find the z -score associated with $0.6$ in the table as:

  $0.25$

This the assembly line will be:

  $\begin{array}{l}x=\overline{x}+z\sigma \\ =1.29+0.25(0.4296)\\ =1.3974\end{array}$

(c)

To determine

To find out what new lower mean time does the company need to achieve.

Answer to Problem 37RE

  $0.8926$ .

Explanation of Solution

It is given in the question that a company that markets build it yourselves furniture sells a computer desk that is advertised with the claim “less than an hour to assemble”. The company has learned that only $25\%$ of its customers succeeded in building the desk in under an hour. The mean time was $1.29$ hours. Thus, to find the new lower mean time does the company need to achieve, we first need to find the z -score associated with $0.6$ in the table as:

  $0.25$

Thus, the mean time is as:

  $\begin{array}{l}x=\overline{x}-z\sigma \\ =1-0.25(0.4296)\\ =0.8926\end{array}$

(d)

To determine

To explain how was that possible.

Explanation of Solution

It is given in the question that a company that markets build it yourselves furniture sells a computer desk that is advertised with the claim “less than an hour to assemble”. The company has learned that only $25\%$ of its customers succeeded in building the desk in under an hour. The mean time was $1.29$ hours. Thus, that is possible because the data were now no longer normally distributed but it is skewed.