Probability Concepts and the Standard Normal Distribution

Hi, I need some assistance with the following two questions. I am not sure that I understand the questions fully. Any assistance would be appreciated.

1. What are some conditions under which business decisions are made using probability concepts? Provide at least two examples of subjective probability.
2. What are the characteristics of Standard Normal Distribution. Explain with examples. Your response should be around 250 words in length.

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Hi, I hope that this helps!

1. Probability theory is used extensively in business. For example, suppose you are planning an outdoor promotion that costs $100,000 and will generate a $30,000 profit. However, there is a 20% chance of rain that day. Should you go ahead with the promotion or cancel due to the chance of rain?

To solve this problem, we do a probability analysis. If it does rain, you will lose $100,000 and if it does not, you will earn $30,000. Thus, your expected profit is (0.2)(-$100,000) + (0.8)($30,000) = -$20,000 + $24,000 = +$4,000. Thus it is worthwhile not to cancel the ...

Solution Summary

We give two examples of how probability theory can be used in business and describe basic properties of the normal distribution. Response includes over 400 words.

Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomial probability as a normalprobability using the continuity correction.
Binomial ProbabilityNormalProbability
c. P ( x ≤ 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ?

Question: A set of 50 data values has a mean of 40 and a variance of 25.
I. Find the standard score (z) for a data value = 47.
II. Find the probability of a data value > 47.
III. Find theprobability of a data value < 47.
Show all work.

1. For a standardized normaldistribution calculate the following probabilities
a. P(0.00 < z < or equal to 2.33)
b. P( -1.00 < z < or equal to 1.00)
c. P( 1.78 < z < 2.34).
2. A random variable is normally distributed with mean of 25 and standard deviation of 5. If an observation is randomly selected
a. what val

Which of the following is not a characteristic of thenormalprobabilitydistribution?
a. It is a discrete probabilitydistribution.
b. The total area under the curve is always equal to 1
c. 68% of the area under thenormal curve is within one standard deviation of the mean.
d. A negative z value is to the

Given a standard normaldistribution, determine the following: Show Table values used.
Given a standard normaldistribution, determine the following: Show Table values used.
a) P( Z < 1.32) =?
b) P(Z>1.32) = ?
c) P(Z<-1.32) =?
d) P(-.30

The diameter of small Nerf balls manufactured at a factory in china is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of 0.08 inches. suppose a random sample of 20 balls are selected, what percentage of sample means will be less than 5.15 inches?

A normaldistribution has a mean of 50 and a standard deviation of 4. Please use Excel Spreadsheets. Show all work and formulas
a) Compute theprobability of a value between 44.0 and 55.0
b) Compute theprobability of a value greater than 55.0
c) Compute theprobability of a value between 52.0 and 55.0

H.) The length of time it takes a student to find a parking spot on campus follows normaldistribution of mean, 3.5 minutes. Theprobability that a student will find a spot in less than 3 minutes is:
1.) 0.8085
2.) 0.1915
3.) 0.3085
4.) 0.6915