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)
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.
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 < 75.0)
(B) P(77.0 lt; x < 83.0)
(C) P(x > 87.0)
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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