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

Summer Morgan · Accepted Answer

Final Answer : D, Explanation :  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.

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