4.7. A counter is set to count gamma rays from a radioactive source. The total number of counts, including background, recorded in each 1-min interval is listed in the accom- panying table. An independent measurement of the background in a 5-min interval gave 58 counts. From these data find: (a) The mean background in a 1-min interval and its uncertainty. (b) The corrected counting rate from the source alone and its uncertainty. Trial 1 2 3 4 5 Total counts 125 130 105 126 128 119 6 7 8 137 9 10 131 115 116