A paracetamol concentration of more than 150 mg per kilogram body weight is considered as dangerous.

The measurements of paracetamol in blood tests are modelled by a random variable with normal

distribution. The standard deviation, linked to the testing method, is supposed to be known and equal to 5

mg. For better assessment, 4 blood tests are usually made. The results are assumed to be independent

realisations of the same normal distribution.

a. On a given patient, the 4 blood tests gave concentrations of 140, 153, 148, and 144. Test whether a

patient is at risk, on view of 4 blood tests using the p-value approach? [12]

b. For the patient of question (a), give a confidence interval. What is your conclusion base on this

confidence interval? [6]