Answer: The probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .
Step-by-step explanation:
The cumulative distribution function for exponential distribution is :-
, where
is the mean of the distribution.
As per given , we have
Average tread-life of a certain brand of tire : 
Now , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles will be :

Hence , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .
Ages of Dan and Cary are 29 and 33 respectively.
<u>Step-by-step explanation:</u>
Step 1:
Form equations out of the given details. Let the age of Dan be x, then age of Cary is x + 4.
In 7 years, sum of their ages = 76
⇒ (x + 7) + (x + 4 + 7) = 76
⇒ 2x + 18 = 76
⇒ 2x = 58
⇒ x = 29
Step 2:
Calculate age of Cary.
⇒ x + 4 = 33