The scores on a standardised aptitude test are assumed to follow a normal distribution with a mean of 50 and a standard deviation of 8.
Using this model, find the probability that a randomly chosen candidate scores more than 65.
A researcher claims that the mean score of candidates from a specific region is higher than 50. A random sample of 64 candidates from this region has a mean score of 52. Test the researcher's claim at the 5% level of significance. You should state your hypotheses clearly.
