Question

(3.29) (a) Use your calculator to find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.32 (0.01) (b) Find the number z such that 35 % of all observations from a standard Normal distribution are greater than z. z (0.01)- (3.33) Automated manufacturing operations are quite precise but still vary, often with distributions that are close to Normal. The width in inches of slots cut by a milling machine follows approximately the N (0.8750, 0.0012) distribution The specifications allow slot widths between 0,8725 and 0,8775 inch. What proportion (+0.001) of slots meet these specifications (use software)?

Answer 1

3.29

a) Here we want to find z such that P( Z < z) = 0.32

Let's use TI-84 calculator:

Command :  

2ND >>> VARS >>>highlight "DISTR" >>>3:invNorm( >>> Then Enter

area : 0.32

: 0

: 1

Then highlight Paste and click on Enter

So we get the following output.

Wabbitemu File View Calculator Debug Help TI-84 Plus Silver Edition TEXAS INSTRUMENTS inYNorm (8.32.0, ト -.4676988012 STAT PLOTF1 TBLSET F2 FORMAT F3 CALC F4 TABLE F 2ND ALOCK ALPHA TEST AANGLE QUIT MODE LINK X.T. STAT INS DEL LIST

Therefore answer is -0.47 after rounding it up to two decimal place.

b) Here we want to find z such that P( Z > z) = 0.35

This implies P(Z < z) = 1 - 0.35 = 0.65

Command :  

2ND >>> VARS >>>highlight "DISTR" >>>3:invNorm( >>> Then Enter

area : 0.65

: 0

: 1

Then highlight Paste and click on Enter

So we get the following output.

Therefore answer is 0.39 after rounding it up to two decimal place.

3.33

Here we want to find P( 0.8725 < X < 0.8775 )

X ~ N( 0.8750, 0.0012)

Command:

2ND >>> VARS >>>highlight "DISTR" >>>2normalcdf( >>> Then Enter

lower : 0.8725

upper: 0.8775

: 0.8750

: 0.0012

Then highlight Paste and click on Enter

So we get the following output.

TI-84 Plus Silver Edition TEXAS INSTRUMENTS normal cdFC , 8725ト 9627792794 STAT PLOTF1 TBLSET F2 FORMAT F3 CALC F4 TABLE F

So answer of this question is 0.9628