Question

Create your own application that would be appropriate for the use of a normal distribution probability analysis to find a probability. Create your own example of a problem that would require you to find the probability with a normal distribution. Describe how you would go about completing the analysis of this problem. Identify the appropriate steps and underlying assumptions of this analysis (cite the textbook as appropriate). Pose a research question that will allow you to work through the example.

Answer #1

Part I: Normal Probability Distribution and Inverse Normal
Probability
You will use Minitab or Excel to answer the following questions. No
hand computation. Minitab users: You can learn about the options
inside the dialogue box of Normal Distribution by calc >
probability distributions > Cumulative Probability > A single
value for form of input > Choose Normal for Distribution >
Enter Value and parameters > Display a table of cumulative
probabilities > OK
Use the ? button in the dialogue...

Draw a normal probability distribution that would allow you to
determine the likelihood of a measure falling within -3SD, -2SD and
-1SD from the mean. Determine the likelihoods of each of the SD’s
on the other side of the mean as well?

Part 1: Use the following steps to create a standard normal in
StatKey and answer the following questions about the variable
Z.
Go to http://www.lock5stat.com/StatKey/
Click on Normal (This is located in the theoretical
distributions section)
Notice in the right hand corner StatKey has a mean of 0 and
standard deviation of 1 as default
Notice in the left hand corner are the usual left, right and 2
tail options these will be helpful in the problems below
For each...

Use the appropriate normal distribution to approximate the
resulting binomial distribution.
A marksman's chance of hitting a target with each of his shots
is 65%. (Assume the shots are independent of each other.) If he
fires 40 shots, what is the probability of his hitting the target
in each of the following situations? (Round your answers to four
decimal places.)
(a) at least 29 times
(b) fewer than 21 times
(c) between 23 and 29 times, inclusive
You may need...

In the following problem, check that it is appropriate to use
the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities.
Ocean fishing for billfish is very popular in the Cozumel region of
Mexico. In the Cozumel region about 41% of strikes (while trolling)
resulted in a catch. Suppose that on a given day a fleet of fishing
boats got a total of 26 strikes. Find the following probabilities.
(Round your answers to four...

Please use a normal distribution X with mean =30 and standard
deviation = 5 (your example) as an example to calculate:
1. P(25<X<35)
2. P(X>50)
3. Find a if (X<a)=0.35
Also, can you think about a reason why the probability in 2.
above is useful?

In the following problem, check that it is appropriate to use
the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities.
Do you take the free samples offered in supermarkets? About 64% of
all customers will take free samples. Furthermore, of those who
take the free samples, about 37% will buy what they have sampled.
Suppose you set up a counter in a supermarket offering free samples
of a new product. The day you...

In the following problem, check that it is appropriate to use
the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities.
Do you take the free samples offered in supermarkets? About 64% of
all customers will take free samples. Furthermore, of those who
take the free samples, about 37% will buy what they have sampled.
Suppose you set up a counter in a supermarket offering free samples
of a new product. The day you...

In the following problem, check that it is appropriate to use
the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities. What's your
favorite ice cream flavor? For people who buy ice cream, the
all-time favorite is still vanilla. About 20% of ice cream sales
are vanilla. Chocolate accounts for only 12% of ice cream sales.
Suppose that 169 customers go to a grocery store in Cheyenne,
Wyoming, today to buy ice cream. (Round...

In the following problem, check that it is appropriate to use
the normal approximation to the binomial. Then use the normal
distribution to estimate the requested probabilities. What's your
favorite ice cream flavor? For people who buy ice cream, the
all-time favorite is still vanilla. About 27% of ice cream sales
are vanilla. Chocolate accounts for only 7% of ice cream sales.
Suppose that 184 customers go to a grocery store in Cheyenne,
Wyoming, today to buy ice cream. (Round...

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