Physicians at a clinic gave what they thought were drugs to 920 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 52 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.48. For the hypotheses that the proportion who improve is 0.48 against that it is greater than 0.48, find the P-value.
P-value =