Question:

1. If the random variable z is the standard normal score and P(z &lt; 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 &lt; -0.37)

(B) P(-1.88 &lt; z &lt; 0)

(C) P(-1.12 &lt; z &lt; 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?

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

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

(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

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answers should be stated to at least three decimal places.