Given a dataset of 40 values with the normal model N(46, 5) approximately how many values should fall between 36 and 46 for the normal model to apply?

Answer 1

In a normal distribution, about 68% of values fall within one standard deviation of the mean. Since the standard deviation is 5 in this case, one standard deviation below the mean (46 - 5 = 41) and one standard deviation above the mean (46 + 5 = 51) should contain approximately 68% of the values.

Therefore, out of 40 values, we would expect approximately 68% of them (0.68 * 40 = 27.2) to fall between 36 and 46 for the normal model to apply. Since we can't have a fraction of a value, we can say that approximately 27 values should fall between 36 and 46 for the normal model to apply.