Scores on a dental anxiety scale range from 0 to 20 the scores are normally distributed with a mean of 11 and a standard deviation of 4. What percentage of the population would have a dental anxiety score greater than 3.

1. Calculate the z-score for x = 3 using the formula:

z = \frac{3 - 11}{4} = -2

2. Look up the cumulative probability for z = -2 in a standard normal distribution table, which is approximately 0.0228.

3. Calculate the probability of a score being greater than 3:

P(X > 3) = 1 - 0.0228 = 0.9772

4. Convert the probability to a percentage:

0.9772 \times 100\% = 97.72\%

Answer: 97.72%