1) The weights of the tomatos is normally distributed. If the middle 83% weigh b
ID: 3130800 • Letter: 1
Question
1) The weights of the tomatos is normally distributed. If the middle 83% weigh between 2.71 ounces and 5.03 ounces, then what is the mean weight of the tomatos?
2) The weights of the potatos is your garden is normally distributed. If the middle 95.44% weigh between 4.82 and 9.21 ounces, then what is the standard deviation of the weights?
3) A visit to a hospital emergency room for something as simple as a sore throat could have a mean cost of $317. Assume that this cost is normally distributed with a standard deviation of $83. What is the cut-off dollar amount if you want to be in the top 3% of the patients?
4) A visit to a hospital emergency room for something as simple as a sore throat could have a mean cost of $316. Assume that this cost is normally distributed with a standard deviation of $88. If you want to be in the bottom 50%, what will be the cut-off dollar amount?
5) A class has 80 students. Test 2 had a class average of 78 and a variance of 49. Answer the following 7 questions. (Assume Normal distribution). Assume a 90-80-70-60 = A-B-C-D scale.
1. What is the probability of getting an A?
2. How many will get an A?
3. What is the probability of getting a B?
4. What is the probability of getting a C?
5. How many people will fail the class?
6. If the bottom 5% will get an F, what will be the cut-off score?
7. If the top 15% get an A, what is the cutoff score for an A?
Explanation / Answer
1.
As these are the middle values, then the mean is exactly in the middle of them, hence,
u = mean = (2.71+5.03)/2 = 3.87 [ANSWER]
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2.
As these are the middle 95.44%, then they are each 2 standard deviations from the mean, by the empirical rule.
Hence, they are 2+2 = 4 standard deviations from each other.
Hence,
sigma = standard deviation = (9.21-4.82)/4 = 1.0975 [ANSWER]
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