The City of Dallas has records indicating that the average daily temperature in the summer is 80 °F, which is normally distributed with a standard deviation of 3 °F.
Based on these records, what is the probability of a daily temperature
- between 75 °F and 87 °F
- between 83 °F and 85 °F
$$P(X<75)=P(Z<-5/3)=0.0485$$ $$P(X<87)=P(Z<7/3)=0.9901$$ $$P(X<83)=P(Z<1)=0.8413$$ $$P(X<85)=P(Z<5/3)=0.9515$$ Am I following the right steps?
How do I interpret my data?
You're on the right track. All that remains for you is to note that $$P(a\le X\le b)=P(X\le b)-P(X\le a)$$ and that this holds for any continuous distribution $X$, including the standard normal distribution $Z$.