Final answer:
The average counting rate is 150 cpm, and the standard deviation, assuming a Poisson distribution, is approximately 12.25.
Step-by-step explanation:
A Geiger counter measures the rate of radioactive decay by counting the number of decay processes per unit time. To find the average counting rate per minute, we divide the total counts by the number of minutes. In this case, we have 750 counts in 5.0 minutes, which results in an average counting rate of 150 counts per minute (cpm).
The standard deviation of the counting rate can be calculated assuming a Poisson distribution, which is appropriate for radioactive decay events. Since the standard deviation in a Poisson distribution is equal to the square root of the mean, the standard deviation here is the square root of 150, which is approximately 12.25.