Characteristics of a Bell Curve; probability calculations, sample confidence

1. Give at least 5 characteristics of the Bell Curve

2. For a normally distributed population, mean of 6.5 and standard
deviation of 4, compute:
a. The probability of picking one item from the population and having it fall between 6.5 and 14.5
b. The probability of picking one item and having it fall above 14.34
c. The point, if the probability of picking an item from the population and having it fall above the point is 2.5%
d. Two points, equidistant from the mean, one to the left of the mean and one to the right that will include 98.98% of the population

3. A sample of 300 is taken and the sample mean is computed to be 7.65 and the sample standard deviation is 5. Assume the data is ratio level.
Compute the 95% confidence interval on the mean.
Compute the 3.9% confidence interval on the mean

Which confidence interval is more practical and useful in a business situation? Why?

1. The total area under a probability distribution graph is equal to _____.
2. The normal distribution is a _____ distribution.
3. Discuss the shape of the normal curve.
4. Define "confidence level" in estimating mu, the population mean.

T and Z tests are parametric tests that are designed to measure the differences in behavior between a sample population and a universal population. How is the T/Z calculation represented on a bell curve? Is it a standard deviation or variance?

How does the bell-shaped curve for the sampling distribution of sample means for samples of size n = 120 compare to the bell-shaped curve for the sampling distribution of sample means for samples of size n = 95?
Answer: A curve with a sample size of 120 will fit a perfect curve more accurately than a curve with a sample size

So, what is the Normal Distribution, and when you think you know what it is, post a real-example of one (other than height), then ask yourself is it really normally distributed? Can everything be normally distributed, that is, fall along a 'bell curve'?

Draw a graph of an insurer's probability distribution for total claim costs, assuming that it has expected claim costs of $500 million. Identify the probability of insolvency if the insurer has assets equal to $750 million.
Please use a Bell Curve.
You are supposed to produce a bell shaped curve, depicting the probability

When dealing with college education one could argue that overall grades received by students follow a normal distribution or bell curve. Hence, grading on a curve (the standard bell curve or normal distribution) might be fair and mirror the overall trend of the student population.
Do you think that this approach is fair?
D

TRUE OR FALSE (With justification)?
If in a probability distribution you got the sum of probabilities less than one, it may mean that you skipped some possible outcome/outcomes.
Health insurance policies are set up in such a way that a healthy person has a negative expected value, and a sickly person has a positive one.

1. This week we learned about normal distributions:
a. Using your own words, tell me what the difference is between a normal distribution and a standard normal distribution.
b. Why do we convert values to z scores to find probability?
2. What is the difference between z scores and area in a bell curve?
3. T / F The n