I would like to calculate the following: the probability of 145 or more successes out of 180 trials in a 2-way choice task. Each trial has an 0.5 probability of success.
I tried to use Excel's BINOMDIST function, calculating this probability as: 1-P(<=144). However, the cumulative probability for this: BINOMDIST(144,180,0.5,TRUE) resulted in 1.
How should I interpret this? What did I do wrong?
Thank you very much in advance!
The normal approximation says you should expect $90$ successes with a standard deviation of $\sqrt {45}\approx 7$ so you are $8$ standard deviations out. The probability of $145$ or more is very small, so when it is subtracted from $1$ you can't see it