Answer:
2.25 %
Explanation:
65-95-99.7 is a rule to remember the precentages that lies around the mean.
at the range of mean ([tex]\mu[/tex]) plus or minus one standard deviation ([tex]\sigma[/tex]), [tex]P([\mu-\sigma \leq X \leq \mu+\sigma])\approx 68.3%[/tex]
at the range of mean plus or minus two standard deviation, [tex]P([\mu -2\sigma \leq X \leq \mu+2\sigma])\approx 95.5%[/tex]
at the range of mean plus or minus three standard deviation, [tex]P([\mu - 3\sigma\leq X \leq \mu+3\sigma])\approx 99.7%[/tex]
So, note that they are asking about the probability that it is greater than 0.32, that is the mean (0.3) plus two times the standard deviation (0.1) ([tex]P(X \leq \mu+2\sigma)[/tex])
So we know that the 95.5% is between [tex]\mu - 2\sigma = 0.3 -2*0.1 = 0.28[/tex] and [tex]\mu + 2\sigma = 0.3 +2*0.1 = 0.32[/tex], hence approximately the 4.5% (100%-95.5%) is greater than 0.32 or less than 0.28. But half (4.5%/2=2.25%) is greater than 0.32 and the other half is less than 0.28.
So [tex]P(X \leq \mu+2\sigma) \approx 2.25%[/tex]
