Give an example from everyday life where you could use the Normal distribution to determine the probability of something.

What is a z score and how could calculating a z help you in a business situation?

How does a box plot relate to the normal distribution? In what ways are they similar? In what ways are they different?

When working with the normal distribution to find probabilities, we often have to subtract the probability value that we found in the table from .5. Why do we do this? What is a good way to remember when to subtract from .5 or not?

Some teachers grade on a curve using the normal distribution to even out the scores. What do you think of this practice?

The answers are in the attached document Answers.doc
They are also given below.

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1. Give an example from everyday life where you could use the Normal distribution to determine the probability of something.

The normal distribution is a commonly occurring distribution in nature and
many random phenomenon roughly approximate this distribution. For example,

1. Modern portfolio theory for stock returns, assumes that the return on a diversified asset portfolio follows a normal distribution. You can thus assume normal distribution and calculate the probability that your return will be greater than a certain value.

2. Distribution of IQ scores can be modeled using a normal distribution. If you want to calculate the probability that a random person in the population has a high IQ (say > 150), you can use the normal distribution table.

2. What is a z score and how could calculating a z help you in a business situation?
In statistics, a standard score indicates how many standard deviations an observation or datum is above or below the mean. It is a dimensionless quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing. Standard scores are also called z-scores.

As one of the common indicators used to measure the stability of a ...

Solution Summary

Give an example from everyday life where you could use the Normal distribution to determine the probability of something.

What is a z score and how could calculating a z help you in a business situation?

Question 1:
When is the mean the best measure of central tendency? When is the median the best measure of central tendency? Explain.
Questions 2:
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Distinguish between discrete and continuous probability distributions. Give an example of each.
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1. Consider a multiple choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 75% probability of answering any question correctly.
a) A student must answer 43 or more questions correctly to obtain a grade A. What percentage

Four symmetrical distributions, labeled (a), (b), (c), and (d), are represented below by their histograms. Without performing any calculations, order the respective standards deviations σ_a, σ_b ,σ_c , and σ_d of the distributions.
A
X X
X X X X
X X

Determine the value of c that makes the function f(x,y) = c(x+y) a joint probability density function over the range:
x greater than 0 and less than 3 and x less than y less than x+2
a) P(X<1, Y<2)
b) P(11)
d) P(X<2, Y<2)
e) E(X)
f) V(X)
g) Marginal probability distribution of X
h) Conditional probabilit

A continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score.
a. x = $1000
b. x = $750
c. x = $1100
d. x = $950
e. x = $1225
2.Using the standard normal table, find the following probabilities

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Could the value of the sample mean and the value of the population mean ever be the same?

Share 1 real-world binomial distribution situation and 1 real-world Poisson distribution situation. Be sure to explain why each example is defined as binomial or Poisson. How would you characterize the difference between the two types of distributions?