Question

Taxpayer	Form 1	Form 2	Form 3	Form 4
1	109	115	126	120
2	98	103	107	108
3	29	27	53	38
4	93	95	103	109
5	62	65	67	64
6	103	107	111	128
7	83	82	101	116
8	122	119	141	143
9	92	101	105	108
10	107	113	127	113
11	103	111	111	108
12	54	64	67	62
13	141	145	142	160
14	92	94	95	102
15	29	32	33	62
16	83	83	89	86
17	34	36	40	48
18	83	86	90	119
19	157	157	172	193
20	99	107	111	100
21	118	123	117	130
22	58	65	75	81
23	66	71	79	81
24	60	60	78	41
25	102	106	100	142
26	128	134	135	142
27	87	93	90	77
28	126	134	129	154
29	133	130	148	164
30	100	112	107	120

Each of the three new forms and the currently used form were filled out by 30 different people. The amount of time (in minutes) taken by each person to complete the task was recorded.

A) If the filling time of all IRS forms is distributed normally with mean of 102 and standard deviation of 8, what is the probability that a randomly selected person could do the tax forms in less than 90 minutes?

B) Referring to problem “A” above, If a randomly selected person is in the top 5 percent of the fastest people who do the tax forms, at least how many minutes should he spent to fill out the form?

Answer 1

a)

µ =    102          
σ =    8          
              
P( X < 90   ) = P( (X-µ)/σ ≤ (90-102) /8)      
=P(Z < -1.50   ) =   0.0668   (answer)

b)

µ=   102                  
σ =    8                  
P(X≤x) =   0.05                  
                      
Z value at    0.05   =   -1.6449   (excel formula =NORMSINV(   0.05   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   -1.645   *   8   +   102  
X   =   88.84   (answer)          

please revert for doubt....