Statistics Question!! Please please please please!!!!!!!!!! solve this problem w

Question

Statistics Question!!

Please please please please!!!!!!!!!! solve this problem with specific explanation and clear handwriting(or typing) please!

If you solve with your handwriting please solve with clear handwriting.....please....Sometimes I can't read you guys handwriting...

Please solve both (a) and (b).

Thanks!

42. Suppose that engineering specifications on the shelf depth of a certain slug to be turned on a CNC lathe are from .0275 in. to .0278 in. and that values of this dimension produced on the lathe can be described using a normal distribution with mean and standard deviation or (a) If Au 0276 and 0001, about what frac tion of shelf depths are in specifications? (b) What machine precision (as measured by o) would be required in order to produce about 98% of shelf depths within engineering spec- ifications (assuming that Au is at the midpoint of the specifications)?

Explanation / Answer

we are given that mean = 0.0276 and sd = 0.0001

and we need to find P(0.275 <X< 0.278)

so we can calculate this using the z score and the z table(please keep them handy)

formula for z scrore is Z = (X-Mean)/SD

(0.0275-0.0.0276)/0.0001 = -1

and likewise (0.0278-0.0.0276)/0.0001 = 2

now P(-1<Z<2), we use the z table as

To find the probability of P (1<Z<2), we use the following formula:

P (1<Z<2 )=P ( Z<2 )P (Z<1 )

We see that P ( Z<2 )=0.9772.

P ( Z<1 ) can be found by using the following fomula.

P ( Z<a)=1P ( Z<a )

After substituting a=1 we have:

P ( Z<1)=1P ( Z<1 )

We see that P ( Z<1 )=0.8413 so,

P ( Z<1)=1P ( Z<1 )=10.8413=0.1587

At the end we have:

P (1<Z<2 )=0.8185 , about 81.85%

b)

now we are given the value as 0.98 for z and we need to find X , using the same Z formula again , we calculate the value of X

0.98 = X - 0.0276)/0.0001

X = 0.98*0.0001 +0.0276 = 0.027698 , would be the required level of precision

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