my questions about radiation protection

1A sample is counted for 30 minutes, and yields 1220 counts. the background count rate for the detector is 5 cpm. a) what are the standard deviation of the gross and background count rates for a 30 min count time?

b)what is the net count rate and its standard deviation?

c)Define a 95% confidence interval for the net count rate ?

2) A detector shows a background count of 500 counts in 30 minute time. what would the LLD for this system be for counting time of:

a)10 minutes.

b)30 minutes

c)10 hours

3)How many counts should be collected in a sample in order to have a 1% error at 95% confidence level?

4) Radioactive sample is counted for 8 min and gives 2300 counts . calculate the count rate and standard deviation for the sample ?

5) Radioactive sample gives an average count of 9390±95 and the counting time for each count is 20±1 min, calculate the average count rate and its standard deviation.