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Question 464993: In an article about the cost of health care, Money magazine reported that a visit to a hospital emergency room for something as simple as a sore throat has a mean cost of $328 (Money, January 2009). Assume that the cost for this type of hospital emergency room visit is normally distributed with a standard deviation of $92. Answer the following questions about the cost of a hospital emergency room visit for this medical service.
What is the probability that the cost will be more than $500? (to 4 decimals)
What is the probability that the cost will be less than $250? (to 4 decimals)
What is the probability that the cost will be between $300 and $400? (in inches, to 4 decimals)
If the cost to a patient is in the lower 8% of charges for this medical service, what was the cost of this patient’s emergency room visit? (to 2 decimals)
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Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Money magazine reported that a visit to a hospital emergency room for something as simple as a sore throat has a mean cost of $328 (Money, January 2009). Assume that the cost for this type of hospital emergency room visit is normally distributed with a standard deviation of $92.
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Answer the following questions about the cost of a hospital emergency room visit for this medical service.
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What is the probability that the cost will be more than $500? (to 4 decimals)
z(500) = (500-328)/92 = 1.8696
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P(x > 500) = P(z > 1.8692) = normalcdf(1.8692,100) = 0.0308
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What is the probability that the cost will be less than $250? (to 4 decimals)
Find the z-value of 250.
Find the probability that z is less than that calculated z-value.
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What is the probability that the cost will be between $300 and $400? (in inches, to 4 decimals)
Find the z-value for 400 and for 300.
Find the probability z is between those calculated values
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If the cost to a patient is in the lower 8% of charges for this medical service, what was the cost of this patient’s emergency room visit? (to 2
decimals)
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Find the z-value with a left-tail of 8%:
invNorm(0.08) = -1.4051
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Solve for "x using x = zs+u
x = -1.4051*92+328
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x = $198.73
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Cheers,
Stan H.
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