Statitics And Probability:-

It is important to control the viscosity of liquid dishwasher soap so that it flows out ofthe container but does not run out too rapidly. Thus, samples are taken randome throughoutthe dag,r and the viscosity.r is measured. Use the following 20 sets of 5 observations for this exercise: Observaliom 1' .l' R 153 147 153 159 169 1511.21] 1'29 E 151 166 151 43 69 1561i] 1 1.05 26 153 174 151 64 35 165.41] 14.33 34 163 141] 1311 1'16 154 163.61] 1652 41] 161] 137 145 164 153 161111] 15.29 42 169 153 149 44 51' 154.41] 9.48 25 156 183 151' 141] 162 159.61] 15.4'1' 43 153 161] 1311 154 1611 16141] 11114 26 164 168 154 53 64 161.61] 555 14 159 153 171] 5% to 1611i] 2.65 1'? 151] 161 169 166 154 1611.11] 1.9? 19 157 138 155 34 65 1491!] 1122 31 161 122 156 45 53 15141] 111111 2'? 143 152 152 156 163 153.21] 1.26 21] 179 157 1215 1'12 143 151.21] 1363 44 154 165 145 52 45 15121] 323 2,1] 171 139 144 54 41' 161.11] 1633 45 137 147 159 16'1' 151 16121] 15.15 41] 153 168 143 33 52 1611!] 1650 4|] 165 155 141] 5'1' 76 1511.61] 1128 36 {a} Calculate the values of 5; 5' and E {1:} Use the values of A3 and sto construct an 3 chart. {at Construct an s chart. {d} Use the values ofA2 and ii chart {e} Construct an R chart. {r} Do the charts indicate that viscosity is in statistical control? Suppose we nd that the number of blemishes in 50foot tin strips averages about F = u. Calculate the control limits. Say the process has gone out of control and this average has increased to 3. {a} What is the probability that the next observation will exceed the UCL'? [h] Wi'lat is the probability that at least 1 of the next 10 observations will exceed the UCL'?