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Question:
 
1. If the random variable z is the standard normal score and P(z < a) = 0.5, then a = 3. Why or why not?
 
2. Given a binomial distribution with n = 14 and p = 0.37, would the normal distribution provide a reasonable approximation? Why or why not?
 
The normal distribution will not provide a reasonable approximation, because the sample size is less than 30 (small-sample). Also, the histogram of the binomial distribution for n = 14
 
with p = 0.37 is considerably skewed to the left, whereas the normal distribution is symmetric.
 
3. Find the area under the standard normal curve for te following:
 
(A) P(z < -0.37)
 
(B) P(-1.88 < z < 0)
 
(C) P(-1.12 < z < 0.48)
 
https://brainmass.com/statistics/all-topics/512836
 
4. Assume that the average annual salary for a worker in the United States is $38,000 and that the annual salaries for Americans are normally distributed with a standard
 
deviation equal to $7,000. Find the following:
 
(A) What percentage of Americans earn below $25,000?
 
(B) What percentage of Americans earn above $46,00?
 
Please show all of your work.
 
Hi,
 
mean = $38,000 and SD = $7000
 
(A) What percentage of Americans earn below $25,000? P(z < -1) = (100-68.27)/2 = 15.87%
 
(B) What percentage of Americans arn above $46,000? P(z > 1) = 15.87%
 
For the normal distribution:
 
one standard deviation from the mean accounts for about 68.27% of the set
 
two standard deviations from the mean account for about 95.4%
 
and three standard deviations from the mean account for about 99.7%.
 
Important to Understand z -values as they relate to the Standard Normal curve:
 
Below: z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.
 
Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50% to the right
 
Running Head: STATS 2
 
5. Find the value of z such that approximately 28.23% of the distribution lies between it and the mean.
 
That z-value has a left-tail of 0.5000-0.2823 = 0.2177
 

 
invNorm(0.2177) = -0.7800
 
—–
 
By symmetry z = +0.7800 is also a solution
 
6. X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:
 
(A) P(x &lt; 75.0)
 
(B) P(77.0 lt; x &lt; 83.0)
 
(C) P(x &gt; 87.0)
 
ISSUE.
 
similar at : https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.405192.html
 
7. Answer the following:
 
(A) Find the binomial probability P(x = 4), where n = 14 and p = 0.60.
 
(B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation.
 
(C) How would you find the normal apprximation to the binomial probability P(x = 4) in part A? Please show how you would calculate µ and σ in the formula for the normal
 
approximation to the binomial, and show the final formula you would use without going through all the calculations.
 
helps extremely: https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.364480.html
 
===
 
Be sure to show your work on the essay-style questions; points will be deducted unless work is shown, and partial credit cannot be awarded unless your reasoning is clear. Numerical
 
answers should be stated to at least three decimal places.

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