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,, 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 against
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 at the 5% level of significance, calculate the minimum possible value for the missing weight, . Give your answer correct to 1 decimal place.