Answer:
a. If the distribution was normal, many values would be negative, what is incompatible with the response variable (hours dedicated to volunteer activities).
b. If the sample is big, accordingly to the Central Limit Theorem, the sampling distribution shape tends to be normally-like, so we can apply a one-sample t-test.
c. The 95% confidence interval for the mean is (13.307, 16.213).
Explanation:
a. If the distribution was normal, the values with one or more standard deviation below the mean would be negative, what is incoherent for this case. This, in a normal distribution, represents approximately 16% of the values.
If we calculate the probabilty for a normal distribution with the sample parameters, the probability of having "negative hours" is 18.6% (see picture attached).
b. If the sample is big, accordingly to the Central Limit Theorem, the sampling distribution shape tends to be normally-like, so we can apply a one-sample t-test.
The sampling distribution standard deviation is also reduced by a factor of 1/√n.
c. We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=14.76.
The sample size is N=500.
When σ is not known, s divided by the square root of N is used as an estimate of σM:

The t-value for a 95% confidence interval is t=1.965.
The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 95% confidence interval for the mean is (13.307, 16.213).