A golfer makes 80% of her putts from a distance of 5 metres or less from the hole. In order to calculate the probability that she would make 23 out of 27 putts or better on a given day, what boundary value should be chosen for X in order to find the appropriate z-score?

Since you want the prob of making 23 or better, you would want the prob that she makes

23 of 27 +24 of 27 + 25 of 27 + 26 of 27 + 27 of 27

you will have 5 prob's to calculate , add them up