Bob is running late for his class and missed his bus. he calls his friend sam to ask for a ride to school. sam, tired of bob interrupting his sleep every week, has lowered the volume of his phone. there is a 70% chance sam sleeps through bob's phone call and does not answer this morning. if sam answers the phone, he will drive to bob's house and give bob a ride. bob will get to school in x minutes, where x follows a (continuous) uniform(15,25) distribution. if sam does not answer the phone, bob has to walk to school. bob is a consistent walker, and will always make it to school in exactly 40 minutes. what is the expected time for bob to get to school today (in minutes)?

The expected time for Bob to get to school today is 34 minutes.

Step-by-step explanation:

We have these following probabilities:

A 70% probability that Sam sleeps through Bob's phone call and does not answer this morning. In this case, Bob has to walk to school. Bob is a consistent walker, and will always make it to school in exactly 40 minutes.

A 30% probability that Sam answers the phone. If Sam answers the phone, he will drive to Bob's house and give Bob a ride. Bob will get to school in X minutes, where X follows a (continuous) Uniform(15,25) distribution.  In this case of an Uniform distribution, the expected time is (15+25)/2 = 20 minutes.

What is the expected time for Bob to get to school today (in minutes)?

There is a 70% probability it takes 40 minutes for Bob to get to school and a 30% probability it takes him 20 minutes. So:

The expected time for Bob to get to school today is 34 minutes.

1/4 because there is 4 grades.