Final answer:
To calculate the percentage of area under a normal curve between two values, we first find the z-scores for those values, then determine the area to the left of each z-score using a z-table or calculator, and finally, subtract the smaller area from the larger area to find the desired percentage.
Step-by-step explanation:
To find the percentage of area under the normal curve between the values of 0.3 and 1.98 for a normal distribution with mean = 1.23 and standard deviation (o) = 0.8, we first need to calculate the z-scores for 0.3 and 1.98.
The z-score formula is z = (X - μ) / o, where X is the value for which we are calculating the z-score, μ is the mean, and o is the standard deviation. The z-score for 0.3 is (0.3 - 1.23) / 0.8 = -1.1625, and for 1.98, it is (1.98 - 1.23) / 0.8 = 0.9375. We then look up these z-scores in a z-table or use a calculator's normal distribution function to find the area to the left of each z-score. The difference between these two areas gives us the percentage of the area under the curve between 0.3 and 1.98.
As the z-table shows a z-score of approximately 1.28 for an area under the normal curve to the left of z of approximately 0.9, we can infer that for a z-score lower than 1.28, the area would be less than 0.9 and for a negative z-score the area to the left would be less than 0.5. So we would need to find the exact areas corresponding to our calculated z-scores and subtract the smaller one from the bigger one to obtain the percentage of the area we are looking for.