Question

A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let x- the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. OSX2 FOX otherwise (a) Find the value of k. (Enter your answer to three decimal places.) 0.375 Draw the corresponding density curve. (Hint: Total area under the graph of f(x) is 1.] f(x) 1.37 1.5 0.5 10 1.5 2.0 0.5 10 15 20 10 0.5 15 20 0.5 * 10 (b) What is the probability that the lecture ends within 1 min of the end of the hour? (Enter your answer to three decimal places.) 0.125 (c) What is the probability that the lecture continues beyond the hour for between 45 and 90 sec? (Round your answer to four decimal places.) 0 3691 (d) What is the probability that the lecture continues for at least 90 sec beyond the end of the hour? (Round your answer to four decimal places.)

Answer 1

(d)

Question asked:

What is the probability that the lecture continues for at least 90 seconds beyond the end of the hour?

Answer:

90 seconds = 1.5 minutes

Р(X > 1.5)— 0.375л? da 1.5

$=\frac{x^{3}}{8}$,

between limits 1.5 to 2

Applying limits, we get:

$P(X\geq 1.5)=\frac{1}{8}(2^{3}-1.5^{3})=\frac{1}{8}(8-3.375)=0.5781$

So,

Answer is:

0.5781