Question

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 62 degrees Upper F to 87 degrees F. What is the probability that a randomly selected August day has a high temperature that exceeded 67 degrees F question mark

Answer 1

`P(X>67)`

And for this case we can use the cumulative distribution function given by:

`F(x) = (x-a)/(b-a) = (x-62)/(87-62) , 62 \leq X \leq 87`

And for this case we can use the complement rule and the cumulative distribution function and we got:

`P(X>67)= 1-P(X<67) = 1- (67-62)/(87-62)= 1-0.2=0.8`

Explanation:

For this case we define the random variable X as "High temperatures in a certain city for the month of August" and the distribution for X is given by:

`X \sim Unif (a=62, b =87)`

And for this case we want to find this probability:

`P(X>67)`

And for this case we can use the cumulative distribution function given by:

`F(x) = (x-a)/(b-a) = (x-62)/(87-62) , 62 \leq X \leq 87`

And for this case we can use the complement rule and the cumulative distribution function and we got:

`P(X>67)= 1-P(X<67) = 1- (67-62)/(87-62)= 1-0.2=0.8`