Chapter 16, Problem 42E

(a)

To determine

To find: the mean and standard deviation for the entire bicycle setup.

Answer to Problem 42E

Mean = 13.54

Median = 3.68

Explanation of Solution

Given:

Suppose

U = unpack time taken

A = assemble time taken

T = tune time taken

Phase	Mean	SD
U	3.5	0.7
A	21.8	2.4
T	12.3	2.7

Formula used:

  $E\left(S\right)=E\left(U+A+T\right)$

  $\mathrm{var}\left(S\right)=\mathrm{var}\left(U+A+T\right)$

  $SD\left(S\right)=\sqrt{\mathrm{var}\left(S\right)}$

Calculation:

Suppose s is total setup time

Mean:

  $\begin{array}{c}E\left(S\right)=E\left(U+A+T\right)\\ =E\left(U\right)+E\left(A\right)+E\left(T\right)\\ =3.5+21.8+12.3\\ =37.6\end{array}$

Variance:

  $\begin{array}{c}\mathrm{var}\left(S\right)=\mathrm{var}\left(U+A+T\right)\\ =\mathrm{var}\left(U\right)+\mathrm{var}\left(A\right)+\mathrm{var}\left(T\right)\\ ={\left(0.7\right)}^2+{\left(2.4\right)}^2+{\left(2.7\right)}^2\\ =13.54\end{array}$

Standard deviation:

  $\begin{array}{c}SD\left(S\right)=\sqrt{\mathrm{var}\left(S\right)}\\ =\sqrt{13.54}\\ =3.68\end{array}$

The overall time for the bike configuration follows a normal model 13.54 and 3.68 average model.

(b)

To determine

To Explain: The bike is set up as promised, ready to go.

Answer to Problem 42E

1.9%

Explanation of Solution

Given:

Suppose

U = unpack time taken

A = assemble time taken

T = tune time taken

Phase	Mean	SD
U	3.5	0.7
A	21.8	2.4
T	12.3	2.7

Calculation:

Required probability

  $\begin{array}{c}P\left(T<30\right)=P\left(Z<\frac{30-37.6}{3.68}\right)\\ =P\left(Z<-2.07\right)\\ =0.019\end{array}$

The possibility that bicycle is setup in an hour is 1.9% because the probability is too less, the bike would not be ready as promised.