An old house in Pomona, CA is inhabited by a variety of ghosts. Ghost appearances occur in the house according to a Poisson process having a rate of 1.4 ghosts per hour. A professor from Cal Poly Pomona has developed a device that can be used to detect ghost appearances. Suppose it is now 1:00 p. m. and the last ghost appearance (the 6th overall) was at 12:35 p. m.
What is the probability that the 7th ghost will appear before 1:30 p. m., to the nearest three decimal places?

The probability is 0.503

Step-by-step explanation:

If the ghost appearances occur in the house according to a Poisson process with mean m, the time between appearances follows a exponential distribution with mean 1/m. so, the probability that the next ghost appearance happens before x hours is equal to:

Then, replacing m by 1.4 ghosts per hour we get:

Additionally, The exponential distribution have a memoryless property, so if it is now 1:00 p.m. and we want the probability that ghost appear before 1:30 p.m., we need to find the difference in hours from 1:00 p.m and 1:30 p.m. no matter that the last ghost appearance was at 12:35 p.m.

Therefore, there are 0.5 hours between 1:00 p.m. and 1:30 p.m, so the probability that the 7th ghost will appear before 1:30 p.m is calculated as:

c is the answer

step-by-step explanation:

900 degrees

step-by-step explanation: