Question

In: Statistics and Probability

6. Suppose that it is known that the mean cost for a certain medical procedure is...

6. Suppose that it is known that the mean cost for a certain medical procedure is $50,000 and that the standard deviation is $13,000.

(a) If you draw a random sample of 45 patients who underwent the same medical procedure, what is the sampling distribution for the sample mean cost based on these 45 patients? Justify your response in one sentence.

(b) What is the probability that the sample mean cost from these 45 patients is between $52,000 and $55,000?

Expert Solution

Solution :

Given that,

mean = = 50000

standard deviation = = 13000

n = 45

(a)

sampling distribution of mean = = = 50000

sampling distribution of standard deviation = / n = = / n = 13000 / 45=1937.9

(b)

= 50000

= / n = 13000 / 45=1937.9

P(52000< <55000 ) = P[(52000-50000) / 1937.9< ( - ) / < (55000-50000) / 1937.9)]

= P(1.03 < Z <2.58 )

= P(Z < 2.58) - P(Z < 1.03)

Using z table,

= 0.9951 -0.8485

probability = 0.1466

orchestra answered 2 years ago

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