To estimate with 95% confidence the mean of a normal population whose standard deviation is assumed to be 4 and the maximum allowable sampling error is assumed to be 1,requires a random sample of size 62.

This is because:
- The formula for calculating the minimum sample size needed for estimating the population mean with a maximum allowable error is:
n = (Zα/2 * σ / E)^2
where Zα/2 is the value from the standard normal distribution for a given level of confidence (in this case, 95% confidence corresponds to Zα/2 = 1.96), σ is the standard deviation of the population, and E is the maximum allowable error.
- Plugging in the given values, we get:
n = (1.96 * 4 / 1)^2 = 61.4656
- Since we need a whole number of samples, we round up to 62. Therefore, a random sample of size 62 is sufficient to estimate the population mean with 95% confidence and a maximum allowable error of 1.