Analyze the data in the following problems using median and up$/$down run tests with z $=\backslash$pm $2.$

a$.$ Given the following run test results of process output, what do the results of the run tests suggest about the process?

Test z$-$score

Median $+1\mathrm{.}37$

Up$/$Down $+1\mathrm{.}05$

multiple choice $1$

Probably random

Probably nonrandom

b$.$ Twenty means were plotted on a control chart. An analyst counted $14$ runs above$/$below the median, and $8$ up$/$down runs. What do the results suggest about the process?

multiple choice $2$

Probably random

Probably nonrandom

c$.$ The following data are the number of defects per spool of cable.

OBSERVATION

$1234567891011121314$

Number of defects $23101320213120$