State the conditions under which a normal distribution can be used as a suitable approximation for a binomial distribution $B(n,p)$.

A wholesale seed distributor claims that 35% of the seeds in their 'Azure Meadow' mix will produce blue-petalled flowers.

Explain why the distributor should not test every seed in a batch to verify this specific claim.

To investigate the distributor's claim, a researcher selects a random sample of 400 seeds and grows them under controlled conditions.

State the null and alternative hypotheses for a two-tailed test of the distributor’s claim.

Of the 400 seeds sampled, 156 were found to produce blue-petalled flowers.

Use a normal approximation to test, at the 5% level of significance, whether there is evidence to suggest the distributor's claim is incorrect.