In a recent year, the distribution of scores of students on the ACT college entrance exam was modelled by a normal distribution with a mean of 20.9 and a standard deviation of 4.7.
1) The mean score of the 84 students at Acme High who took the ACT that year was 23.
a) What is the probability that the mean score for 84 students selected randomly from all who took the test nationally is 23 or higher?
b) The people at Acme believe they scored significantly higher than the nation as a whole. Test this hypothesis at the 0.01 level.
for 1a) I tried using normalcdf(23, 1x10^99, 20.9, 4.7/√ 84) but I was getting a very small answer, I tried computing the z score as well using ->
(sample mean - mean) / (standard deviation of population / square root of n)
However, these values didn't really make sense to me and thus I wasn't able to find an answer and determine wether it conforms to the 0.01 level. Please help!