Question

P(Z<z)	z		Mu	Sigma	x
0.2735		FALSE	202	65		FALSE
0.8615		FALSE	543	60		FALSE
0.0790		FALSE	352	244		FALSE
0.3020		FALSE	552	348		FALSE
0.4139		FALSE	787	255		FALSE
0.9537		FALSE	643	499		FALSE
0.9127		FALSE	949	60		FALSE
0.7930		FALSE	68	66		FALSE
0.4808		FALSE	246	205		FALSE
0.3821		FALSE	-93	4		FALSE
0.3747		FALSE	256	50		FALSE
0.0671		FALSE	-123	6		FALSE
Instructions:	Complete columns B and F. Don't round column F.
Notes:	Skill with no specific practice set: Finding z and x for P(Z>z). These must be found by either subtracting from 1 or reversing sign of z.

Answer 1

Solution:

We are given that:

P(Z< z) and we have to find corresponding z values.
Also we are given that mean and Standard deviation values and we have to find corresponding x values.

We use excel command to find z values:

=NORM.S.INV( Probability )

=NORM.S.INV( 0.2735)

= -0.60226

= - 0.60

and for x values we use formula:

=NORM.INV( probability , Mean , SD )

=NORM.INV( 0.2735 , 202 , 65 )

=162.853

Or we can use Formula:

Thus we get:

P(Z<z)	z		Mu	Sigma	x
0.2735	-0.60226	FALSE	202	65	162.853	FALSE
0.8615	1.08708	FALSE	543	60	608.225	FALSE
0.079	-1.41183	FALSE	352	244	7.513	FALSE
0.302	-0.51866	FALSE	552	348	371.507	FALSE
0.4139	-0.21752	FALSE	787	255	731.531	FALSE
0.9537	1.68184	FALSE	643	499	1482.238	FALSE
0.9127	1.35757	FALSE	949	60	1030.454	FALSE
0.793	0.81687	FALSE	68	66	121.914	FALSE
0.4808	-0.04815	FALSE	246	205	236.130	FALSE
0.3821	-0.29997	FALSE	-93	4	-94.200	FALSE
0.3747	-0.31943	FALSE	256	50	240.028	FALSE
0.0671	-1.49774	FALSE	-123	6	-131.986	FALSE

To find x for P( Z > z) use following steps:

reverse the sign of z values and use these z values to find x values:

P(Z<z)	z	new z		Mu	Sigma	x
0.2735	-0.60226	0.60226	FALSE	202	65	241.147	FALSE
0.8615	1.08708	-1.08708	FALSE	543	60	477.775	FALSE
0.079	-1.41183	1.41183	FALSE	352	244	696.487	FALSE
0.302	-0.51866	0.51866	FALSE	552	348	732.493	FALSE
0.4139	-0.21752	0.21752	FALSE	787	255	842.469	FALSE
0.9537	1.68184	-1.68184	FALSE	643	499	-196.238	FALSE
0.9127	1.35757	-1.35757	FALSE	949	60	867.546	FALSE
0.793	0.81687	-0.81687	FALSE	68	66	14.086	FALSE
0.4808	-0.04815	0.04815	FALSE	246	205	255.870	FALSE
0.3821	-0.29997	0.29997	FALSE	-93	4	-91.800	FALSE
0.3747	-0.31943	0.31943	FALSE	256	50	271.972	FALSE
0.0671	-1.49774	1.49774	FALSE	-123	6	-114.014	FALSE