Mean mass of normally distributed loaves from the percentage below a mass, then a one-tailed test after a change of recipe

A bakery makes loaves of bread whose masses are normally distributed with standard deviation \(15\) grams. Records show that \(20\%\) of the loaves have a mass of less than \(400\) grams.

1. Show that the mean mass of the loaves is \(412.6\) grams, correct to \(1\) decimal place.[3]

The bakery changes its recipe with the aim of making heavier loaves. The standard deviation is unchanged. A random sample of \(36\) loaves made with the new recipe has a mean mass of \(416.4\) grams. The null hypothesis is \(\mathrm{H}_0\): the mean mass of the loaves is unchanged by the new recipe.

2. State the alternative hypothesis, \(\mathrm{H}_1\).[1]
3. State, with a reason, whether a one-tailed or a two-tailed test should be used.[2]
4. Determine whether the new recipe has significantly increased the mean mass, at the \(5\%\) significance level.[4]