State the conditions under which the Normal distribution can be used as an approximation to the Binomial distribution.

A marine biologist claims that the proportion of leatherback turtle hatchlings that successfully reach the ocean from their nests is 0.42. A local conservationist believes that a new beach-lighting initiative has improved this survival rate.

State suitable null and alternative hypotheses to test the conservationist's belief.

To investigate this claim, a random sample of 150 hatchlings is observed, and it is found that 75 of them successfully reached the ocean.

Using a suitable approximation, test at the 5% level of significance whether or not there is evidence to support the conservationist's belief.