Question 10 of 12 (1 point) View problem in a pop-up The average yearly Medicare

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Question 10 of 12 (1 point) View problem in a pop-up The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year Suppose the benefits are normally distributed with a standard deviation of $460. Assume that the sample is taken from a large population and the correction factor can be ignored. Use a graphing calculator and round the answer to four decimal places Source: New Jork Times Almanac. Part 1 Find the probability that the mean benefit for a random sample of 20 patients is more than 54225. P (N > 4225)-E-0532 Correct answer Parr 2 our ofz Find the probabiliry that the mean benefit for r a random sample of 20 patients is less than $3950.

Explanation / Answer

Solution:- mean = 4064 , sd = 460

part1:-

P(X > 4225) = P( Z > (4225 - 4064)/(460/sqrt(20))

= P( Z > 1.5652)

=  0.0582

part 2:-

   P(X < 3950) = P( Z < (3950 - 4064)/(460/sqrt(20))

= P( Z < -1.1083)

= 0.1335

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