Compute the Expected Age $\mu$ Of a British Nurse in 1851

Multiple Choice

Compute the expected age $\mu$ of a British nurse in 1851. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth. $$\begin{array} { | l | c | c | c | c | c | c | c | } \hline \text { Age range (yr) } & \mathbf { 2 0 } - \mathbf { 2 9 } & \mathbf { 3 0 } - \mathbf { 3 9 } & \mathbf { 4 0 } - \mathbf { 4 9 } & \mathbf { 5 0 } - \mathbf { 5 9 } & \mathbf { 6 0 - 6 9 } & \mathbf { 7 0 } - \mathbf { 7 9 } & \mathbf { 8 0 } + \\\hline \text { Midpoint } ( x ) & 24.5 & 34.5 & 44.5 & 54.5 & 64.5 & 75.5 & 84.5 \\\hline \text { Percent of nurses } & 5.6 \% & 9.8 \% & 19.4 \% & 29.2 \% & 25.1 \% & 9.1 \% & 1.8 \% \\\hline\end{array}$$

A) 54.50
B) 59.50
C) 53.85
D) 53.88
E) 43.88