Question

The time between phone calls at Jawwal center has an exponential distribution with an average of 40 seconds. What is the probability that the time is at least 55 seconds?

a) 0.2528
b) 0.4832
c) 0.4169
d) 0.7472
e) 0.3189

Answer 1

To find the probability that the time between phone calls at Jawwal center is at least 55 seconds, we can use the exponential distribution. The probability can be calculated as 1 minus the probability that the time between calls is less than or equal to 55 seconds. The probability is 0.7472.

Step-by-step explanation:

To find the probability that the time between phone calls is at least 55 seconds, we can use the exponential distribution. The exponential distribution is determined by the average time between events, which in this case is 40 seconds.

The probability that the time between calls is at least 55 seconds can be calculated by subtracting the probability that the time between calls is less than or equal to 55 seconds from 1. Using the formula for the exponential distribution, P(T < t) = 1 - e^(-λt), where λ is the average rate of events per unit of time and t is the desired time interval, we can calculate the probability.

First, we need to calculate the rate parameter λ using the average time between calls. λ = 1/average time = 1/40 = 0.025.

Next, we substitute the values into the formula: P(T > 55) = 1 - P(T <= 55) = 1 - (1 - e^(-0.025 * 55)) = 0.7472.

Therefore, the probability that the time between phone calls at the Jawwal center is at least 55 seconds is 0.7472.