A normal distribution has a meaning of 50 and a standard deviation of 6. What is the probability that a value selected at random from this data is in the interval from 50 to 62? Express your answer as a percent rounded to the nearest 10th

We first need to standardise the value X=50 and X=62, in other words, find the z-scores.

The formula to find z-score is (X-μ) / σ

Where μ is the mean score which in this case is 50 and σ is the standard deviation = 6

Z-score for X = 50 ⇒ (50-50) : 6 = 0:6 = 0

Z-score for X = 62 ⇒ (62-50) : 6 = 12:6 = 2

Presenting this information on a normal distribution bell curve, the area we need is in between z = 0 and z = 2

P (0
P (0
P (0
As a percentage, the probability is 0.4772 * 100 = 47.72%