Find the area between x = 9.5 and x = 23 under a normal distribution curve with μ = 20 and σ = 4 .

Question

normal distribution curve

Answer 1

Work out z-score for x=9.5 and 23 with mean=20 and SD=4: (9.5-20)/4=-10.5/4=-2.625 and (23-20)/4=3/4=0.75.
The corresponding values from a normal distribution table are 0.00435 and 0.2734. These are cumulative probabilities for two z values and they represent the area under the distribution curve. The difference between them is the area under the curve between the given x values=0.2734-0.0044=0.2690. The answer is also the cumulative probability of a data result being between the given limits.