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Random Variable Is Normally Distributed With A Mean

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Random variable is normally distributed...

Random variable is normally distributed with a mean of μ = 50 and a standard deviation of σ = 5.

What is the probability the random variable will assume a value between 45 and 55 (to 4 decimals)?

What is the probability the random variable will assume a value between 40 and 60 (to 4 decimals)?

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)

{Exercise 6.21}

A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society (US Airways Attache, September 2000).

If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa (to the nearest whole number)?

Submitted: 6 years ago.Category: Homework
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10/13/2011
Tutor: R.R. Jha, Tutor replied 6 years ago
R.R. Jha
R.R. Jha, Tutor
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Hi,
Answers below are marked in bold below each question.

Random variable is normally distributed with a mean of μ = 50 and a standard deviation of σ = 5.
What is the probability the random variable will assume a value between 45 and 55 (to 4 decimals)?
0.6827

What is the probability the random variable will assume a value between 40 and 60 (to 4 decimals)?
0.9545

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)
0.0308

What is the probability that the cost will be less than $250? (to 4 decimals)
0.1983

What is the probability that the cost will be between $300 and $400? (in inches, to 4 decimals)
0.4026

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)
198.73

{Exercise 6.21}
A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society (US Airways Attache, September 2000).

If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa (to the nearest whole number)?
131

Let me know if any question
Regards
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Customer reply replied 6 years ago
Its showing that these problems are wrong, Its a computer program that I insert the answers in to. Everything else is correctWhat 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)
Tutor: R.R. Jha, Tutor replied 6 years ago
Checked again, these should be correct. Please check if the mean and standard deviations for the questions are same as intended, otherwise it might be rounding error. For first error, try 0.1982 and let me know.
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Customer reply replied 6 years ago
You were correct, just went to professors office, computer program is having problems and she will adjust the points. Thank you for your help.
Tutor: R.R. Jha, Tutor replied 6 years ago
You're welcome!
Let me know if you've more questions.
Ask Your Own Homework Question
Customer reply replied 6 years ago
Just got an email from professor, computer was fine, the answers are wrong but not because you did them wrong, you were to precise, "Your answers are actually more accurate than the Table
method expects. Round z values to 2 decimal places and use those.
When going in the reverse direction find the closest probability and use
its z value. for the following questions
What is the probability that the cost will be less than $250? (to 4 decimals)
0.1983
What is the probability that the cost will be between $300 and $400? (in inches, to 4 decimals)
0.4026
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)
198.73
Tutor: R.R. Jha, Tutor replied 6 years ago
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