- #1
archaic
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- Homework Statement
- In a lab, the reaction time of the students to an event related to the experiment they are conducting is normally distributed with ##\mu=0.5## seconds, and ##\sigma=0.05## seconds.
1) What is the probability that a student will react after more than ##0.5## seconds?
2) What is the probability that a student's reaction time falls between ##0.45##, and ##0.55## seconds?
3) What is the reaction time that is exceeded ##90\%## of time?
- Relevant Equations
- .
1) ##P(X>0.5)=P(Z>0)=0.5##
2) ##P(0.45<X<0.55)=P(X<0.55)-P(X<0.45)=P(Z<1)-P(Z<-1)\approx68\%##
3) ##P(X>x)=0.9\Leftrightarrow P(Z>\frac{x-0.5}{0.05})=0.9\Leftrightarrow1-P(Z\leq\frac{x-0.5}{0.05})=0.9\Leftrightarrow P(Z\leq\frac{x-0.5}{0.05})=0.1##
I find that ##\frac{x-0.5}{0.05}=-1.28##, which gives me ##x=0.436##.
Correct? Thank you!
2) ##P(0.45<X<0.55)=P(X<0.55)-P(X<0.45)=P(Z<1)-P(Z<-1)\approx68\%##
3) ##P(X>x)=0.9\Leftrightarrow P(Z>\frac{x-0.5}{0.05})=0.9\Leftrightarrow1-P(Z\leq\frac{x-0.5}{0.05})=0.9\Leftrightarrow P(Z\leq\frac{x-0.5}{0.05})=0.1##
I find that ##\frac{x-0.5}{0.05}=-1.28##, which gives me ##x=0.436##.
Correct? Thank you!