Hey frantastic.

When you say 84 is that a percentile? (In other words, is the score in the lower 84% of scores for the normal distribution)?

If this is the case calculate the test statistic z = (11.3 - 17.8)/sd and find using either tables or a computer P(Z < z).

We can definitely say that it will be in the bottom 50% since 11.3 < 17.8 so it will definitely be in the bottom 84%.