The graph to the right is the uniform probability density function for a friend who is $x$ minutes late. (a) Find the probability that the friend is between 5 and 30 minutes late. (b) It is 10 A.M. There is a $10 \%$ probability the friend will arrive within how many minutes? (a) The probability that the friend is between 5 and 30 minutes late is (Type an integer or a decimal. Round to three decimal places as needed.)

Step 1 ：The problem is asking for the probability that the friend is between 5 and 30 minutes late. Since this is a uniform distribution, the probability is simply the length of the interval divided by the total length of the distribution.

Step 2 ：In this case, the total length of the distribution is not given, but we can assume it to be 60 minutes (as it is common to consider lateness in terms of an hour).

Step 3 ：Therefore, the probability is calculated as \((30-5)/60 = 25/60\).

Step 4 ：Simplifying the above expression gives a probability of \(0.4166666666666667\).

Step 5 ：Rounding to three decimal places, the final answer is \(\boxed{0.417}\).