In an article in Quality Engineering, a research article presented individual measurement data on sand compactibility. Measurement data on $10$ measurements is presented in Table $6\mathrm{.}1.$

Table $6\mathrm{.}1$: Results from samples of $10$ measurements for sand compactibility

Sample

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$9$

$10$

Mean

$46$

$43$

$41$

$42$

$40$

$44$

$40$

$41$

$40$

$42$

For these data, the author reported that the lower and upper specifications for sand compactibility are $38$ and $46,$ respectively. The standard deviation for the sand compactibility process is $1\mathrm{.}87$ and the company is aiming for $3$ sigma performance$($critical value for the ratio of $1\mathrm{.}0).$

Calculate:

The capability index Blank $1$

The capability ratioBlank $2$

Is the sand compactibility process capable? Please choose YES or NO$.$