Suppose the incubation period for land turtle eggs is normally distributed with a mean of sixty-seven days and standard deviation of 7.4 days:

(a)Find the probability that a land turtle egg will take at least eighty days to hatch.

(b)Find the probability that a land turtle egg will take at most fifty-five days to hatch

(c)find the probability that a land turtle egg will take between fifty and eighty-five days to hatch.

(d) find the length of time such that 85% of the land turtle eggs will have hatched by then.

(e) suppose a veterinarian becomes concerned about the health of the land turtle if it takes longer than ninety days to hatch. What is the probability of this happening if the turtle is healthy? Is it likely for this to happen?

(f) Find and interpret the 90th percentile.