Calculus and Above

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would the normal distribution provide...

1) Given a binomial distribution with n = 29 and p = 0.83, would the normal distribution provide a reasonable approximation? Why or why not?

2) Find the value of z such that approximately 8.32% of the distribution lies between it and the mean.

3) If the random variable z is the standard normal score, is it true that P(-3 < z 1? Why or why not?

4) Find the area under the standard normal curve for the following:

(A) P(z > 2.06)

(B) P(0 < z < 0.18)

(C) P(-1.31 < z < 1.09)

5) Assume that the average annual salary for a worker in the United States is $35,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,500. Find the following:

(A) What percentage of Americans earn below $26,000?

(B) What percentage of Americans earn above $40,000?

Please show all of your work.

6) 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 approximation 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. (Points : 6)

7) 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(75.0 < x 89.0)

2) Find the value of z such that approximately 8.32% of the distribution lies between it and the mean.

3) If the random variable z is the standard normal score, is it true that P(-3 < z 1? Why or why not?

4) Find the area under the standard normal curve for the following:

(A) P(z > 2.06)

(B) P(0 < z < 0.18)

(C) P(-1.31 < z < 1.09)

5) Assume that the average annual salary for a worker in the United States is $35,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,500. Find the following:

(A) What percentage of Americans earn below $26,000?

(B) What percentage of Americans earn above $40,000?

Please show all of your work.

6) 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 approximation 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. (Points : 6)

7) 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(75.0 < x 89.0)

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