The instructions to label the distribution probably are suggesting that you use the empirical (68-95-99.7) rule. It's the one that says approximately 68% of a normal distribution lies within 1 standard deviation of the mean, 95% within 2 standard deviations of the mean, and 99.7% with 3 standard deviations of the mean.
Suppose [tex]X[/tex] represents the random variable for the number of days a house is on the market. Then what the above means is that for this particular distribution
[tex]\mathbb P(|X-50|\le13)=\mathbb P(37\le X\le63)\approx0.68[/tex]
[tex]\mathbb P(|X-50|\le26)=\mathbb P(24\le X\le76)\approx0.95[/tex]
[tex]\mathbb P(|X-50|\le39)=\mathbb P(11\le X\le89)\approx0.997[/tex]
Using these probabilities, and the fact that the distribution is symmetric, you would find
5. 99.7%, following immediately from the rule;
6. 84%. The distribution is symmetric, so exactly 50% falls to either side of the mean. This also means we can split up [tex]\mathbb P(37\le X\le 63)=0.68[/tex] to find that [tex]\mathbb P(37\le X\le50)=0.34[/tex];
7. 68%, again straight from the rule;
8. 2.5%. About 95% of houses are on the market between 24 and 76 days, so 5% are not. Half of these are on the market for less than 24 days.
