Respuesta :
The total number of holes will be (a)15 and (b) 4 when the drilling machine is used whose standard deviation is 0.0028mm.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
The sum of all values divided by the total number of values constitutes a dataset's mean.
The mean of the holes are given as 4.05 mm([tex]\mu=4.08[/tex])
The standard deviation is given as 0.0028 mm([tex]\rho=0.0028[/tex])
Now we will use the z-score and probability distribution to calculate the frequency of the holes to have diameter between 4.048 and 4.0553.
Here [tex]Pr(4.048\leq X\leq 4.0053)[/tex] ,so we need to compute the z-values
[tex]Z_1=\frac{X_1-\mu}{\rho} \\Z_1=\frac{4.048-4.05}{0.0028} \\Z_1=-0.7143[/tex]
Similarly:
[tex]Z_2=1.8929[/tex]
Therefore from the above statements we can say that
[tex]Pr(-0.7143\leq X\leq 1.8929)[/tex]
Solving for probability distribution we get
[tex]Pr(4.048\leq X\leq 4.0053)=0.7333[/tex]
Total number of holes=0.7333 × 20= 14.666..
Therefore the number of holes is 15
Similarly
The z-value corresponding to 4.052 mm is given by 0.71
The z-value corresponding to 4.056 mm is given by:2.14
The probability of the diameter being between 4.052 mm and 4.056 mm is 0.4838 – 0.2611 =0.2227
The number likely to have a diameter between 4.052 mm and 4.056 mm = 0.2227 × 20
= 4.454
= 4, correct to nearest whole number
To learn more about standard deviation:
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