Question

The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medicare service. For this group, 40% of first round appeals were successful (The Wall Street Journal, October 22, 2012). Suppose ten first round appeals have just been received by a Medicare appeals office.

What is the expected value for this experiment?

What is the standard deviation for this experiment?

Answer 1

it is given that sample size n = 10 with probability p = 40% = 40/100 = 0.40

we know mean or expected value = n * p

where n = 10 and p = 0.40

this gives, expected value = 10*0.4 = 4

And

standard deviation = sqrt{n*p*q}............................where sqrt is square root function

we have n = 10, p=0.4 and q = 1-p = 1-0.4 = 0.6

setting the values, we get

standard deviation = sqrt{10*0.4*0.6}

= sqrt{2.4}

= 1.55

So, expected value is 4 and standard deviation is 1.55