About 30% of the population cannot detect any odor when they sniff the steroid androstenone, but they can become sensitive to its smell if exposed to the chemical repeatedly. does this change in sensitivity happen in the nose or the brain? mainland et al. (2002) exposed one nostril of each of 12 non-detector participants to androstenone for short periods every day for 21 days. the other nostril was plugged and had humidified air flow to prevent androstenone from entering. after the 21 days, the researchers found that 10 of 12 participants had improved androstenone-detection accuracy. this suggested that increases in the plugged nostril, whereas two had reduced accuracy. this suggested that increases in sensitivity to androstenone happened in the brain rather than in the nostril, since the epithelia of the nostrils are not connected. the authors conducted a statistical hypothesis test of whether accuracy in fact did change. let p refer to the proportion of non-detectors in the population whose accuracy scores improve after 21 days. under the null hypothesis, p = 0.5 (as many participants should improve as deteriorate in their accuracy after 21 days). the alternative hypothesis is that p is not equal to 0.5. what is the probability of obtaining a value of 10 or greater? express with four significant figures, and include the leading zero.