P (54 < x < 64)
There are successes between 54 and 64 (both not inclusive). It is denoted as P(54 < x < 64)
The possible discrete midpoint values for the given binomial distribution range from 55, 56, …, 62, 63.
To convert the discrete values to a continuous interval, we need to do a continuity correction and to move 0.5 unit to either side of the discrete midpoint value to include all possible x values.
Thus, the corresponding interval for normal distribution probability is 54.5 < x < 63.5.