1. Pizza Prince is a fast-food restaurant which is known for their Crown pizza.  The weights of Crown pizza are normally distributed with standard deviation 42 g.  It is thought that the mean weight,$\mu$, is 350 g.

A restaurant inspector believes that the mean weight of the Crown pizza is less than 350 g.  She visits the restaurant over the period of a week, and samples and weighs five randomly selected Crown pizzas.  She uses the data to carry out a hypothesis test at the 5% level of significance.

She tests ${H}_{0}∶ \mu =350$  against  ${H}_{1}∶ \mu <350.$

When the inspector writes up her report, she can only find the values for four of the weights, these are shown below:

325.2              356.1              319.7              300.5

Given that the result of the hypothesis test is that there is insufficient evidence to reject ${H}_{0}$ at the 5% level of significance, calculate the minimum possible value for the missing weight, $w$. Give your answer correct to 1 decimal place.