The following is the probability distribution for the number of daily requests a health secretary receives for a health clearance.

Question

Find the expected daily number of health clearance requests and the standard deviation of the daily number health clearance requests.

NUMBER OF REQUESTS ----- PROBABILITY

0 0.02

1 0.25

2 0.33

3 0.17

4 0.14

5 0.09

Answer 1

The expected value of a probability distribution is calculated by multiplying each value by its probability and taking the sum of the products; in this case

E(x) = 0(0.02)+1(0.25)+...+5(0.09)

The standard deviation is then calculated by:

1) calculating the deviation of each value (x) from the expected value E(x),

2) squaring this value

3) multiplying the square by the probability

4) taking the sum of steps 1-3 for each value

5) taking the square root of the resulting sum

In this case, (n= the number of values, in this case 6)

δ(x) = sqrt(∑₁ⁿ([x_n-E(x)]²*p))

= sqrt(([0-E(x)]²*0.02)+([1-E(x)]²*0.25)+...+([5-E(x)]²*0.09))