The number of emergency calls received by a switchboard in an hour has an expected value of 0.5 and a standard deviation of 0.7.Find the mean and standard deviation of the number of emergency calls received by the switch board during a workshift lasting 4 hours.Assume that the hours are independent of each other.
A)μ = 2,σ = 11.2
B)μ = 1.00,σ = 2.8
C)μ = 2,σ = 2.8
D)μ = 2,σ = 1.40
E)μ = 1.00,σ = 1.40

Question

Quizplus · Accepted Answer

The mean of the number of emergency calls received by switchboard during a 4-hour shift is the sum of the means of the hourly calls, which is (0.5 x 4) = 2.

The variance of the number of emergency calls received by switchboard during a 4-hour shift is the sum of the variances of the hourly calls, which is (0.7 x 0.7 x 4) = 1.96.

Therefore, the standard deviation of the number of emergency calls received by switchboard during a 4-hour shift is sqrt(1.96) = 1.40.

Choice D is the only option that has the correct values for both the mean and the standard deviation.

The Number of Emergency Calls Received by a Switchboard in an Hour