Distribution of x on a Symmetrical Shape

Let x be a random variable. The x distribution has a mean of 16 days. SD= 2 days
The distribution of x values is more or less mound shaped and symmetrical but not necessarily normal. N=30 number of eggs in an incubator. Let x(with a line over it) be the average incubation times of eggs.

a. what can we say about the probability distribution of x(with a line over it)? Is it approximately normal? What are the mean and standard deviation?
b. What is the probability that x(with a line over it) is between 16 and 17 days?
c. What is the probability that x(with a line over it) is less than 15 days?

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