Question

The average yearly Medicare Hospital Insurance benefit per person was $4604 in a recent year with standard deviation of $460. In sixty-seven percent of the cases, the Medicare Hospital Insurance benefit is less than a certain amount “E”. Find the amount of “E”.

Answer 1

Let the random variable denoting average yearly Medicare Hospital Insurance benefit per person be be X.

So, X ~ N(4604 , 460²)

The amount E for which 67% of the Medical Hospital benefit will be less than this amount =

P(X < E) = 0.67

P(Z < (E-4604)/460) = 0.67

Using Standard distribution table, we get,

(E-4604)/460 = 0.440

E =( 0.440*460) + 4604

E = $4806.4

So, the amount E, below which there are sixty seven percent of the benefits is $4806.4.

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