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Chapter 6 00. The average rent...

Chapter 6

00. The average rent in a city is $1,570 per month with a standard deviation of $200. Assume rent follows the normal distribution. Use the empirical rule to answer the following questions.

a.What percentage of rents are between $1,370 and $1,770? (Round your answer to 2 decimal places.)

Percentage of rents ______%

b.What percentage of rents are less than $1,370? (Round your answer to 2 decimal places.)

Percentage of rents _______ %

c.What percentage of rents are greater than $1,970? (Round your answer to 2 decimal places.)

Percentage of rents ______ %

0. A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag is a uniformly distributed random variable that ranges from 6.9 to 11.9 pounds.

a. Calculate the expected value and standard deviation of this distribution. (Do not round intermediate calculations. Round your "expected value" to 2 decimal places and "standard deviation" answer to 4 decimal places.)

Expected value = ________ Standard deviation= _____________

b. Find the probability that the weight of a randomly selected bag is no more than 8.3 pounds. (Do not round intermediate calculations. Round your answer to 2 decimal place.)

Probability__________

c. Find the probability that the weight of a randomly selected bag is at least 7.4 pounds. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Probability= _____________

1. A random variable X is exponentially distributed with an expected value of 36.

a-1.What is the rate parameter λ? (Round your answer to 3 decimal places.)

Rate parameter λ = ______________

a-2.What is the standard deviation of X?

Standard deviation = ____________

b. Compute P(29 ≤ X ≤ 43). (Round your intermediate calculations and final answer to 4 decimal places.)

P(29 ≤ X ≤ 43)=__________

c. Compute P(24 ≤ X ≤ 48). (Round your intermediate calculations and final answer to 4 decimal places.) P(24 ≤ X ≤ 48)= __________

2. The random variable X is normally distributed. Also, it is known that P(X > 186) = 0.03. Use Table 1. http://lectures.mhhe.com/connect/0073361615/Table/table1.jpg

a.Find the population mean μ, if the population standard deviation σ = 11. (Round "z" value to 2 decimal places and final answer to 2 decimal place.)

Mean=

b.Find the population mean μ, if the population standard deviation σ = 22. (Round "z" value to 2 decimal places and final answer to 2 decimal place.)

Mean =

c.Find the population standard deviation σ, if the population mean μ = 165. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

Standard deviation =

d.Find the population standard deviation σ, if the population mean μ = 153. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

Standard deviation =

3. The historical returns on a balanced portfolio have had an average return of 6% and a standard deviation of 8%. Assume that returns on this portfolio follow a normal distribution. Use the empirical rule to answer the following questions.

a.What percentage of returns were greater than 22%? (Round your answer to 2 decimal places.)

Percentage of returns_________ %

b. What percentage of returns were below −18%? (Round your answer to 2 decimal places.)

Percentage of returns__________ %

4. A random variable X follows the continuous uniform distribution with a lower bound of −7 and an upper bound of 14.

a. What is the height of the density function f(x)? (Round your answer to 4 decimal places.) f(x) =

b. What are the mean and the standard deviation of the distribution? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Mean =________ Standard deviation = ________

c. Calculate P(X ≤ −2). (Round your intermediate calculations and final answer to 4 decimal places.)

P(X ≤ −2)=

5. A random sample of size n = 241 is taken from a population of size N = 5,588 with mean μ = −68 and variance σ2 = 183. Use Table 1. http://lectures.mhhe.com/connect/0073361615/Table/table1.jpg

a-1. Calculate the expected value and the standard deviation of the sample mean. (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round "standard deviation" to 2 decimal places.) Expected value = -68 Standard deviation____________

b. What is the probability that the sample mean is between −70 and −66? (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability___________

c. What is the probability that the sample mean is greater than −67? (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability_______

6. A random sample of size n = 36 is taken from a population with mean μ = −6.8 and standard deviation σ = 3. Use Table 1.

b. What is the probability that the sample

00. The average rent in a city is $1,570 per month with a standard deviation of $200. Assume rent follows the normal distribution. Use the empirical rule to answer the following questions.

a.What percentage of rents are between $1,370 and $1,770? (Round your answer to 2 decimal places.)

Percentage of rents ______%

b.What percentage of rents are less than $1,370? (Round your answer to 2 decimal places.)

Percentage of rents _______ %

c.What percentage of rents are greater than $1,970? (Round your answer to 2 decimal places.)

Percentage of rents ______ %

0. A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag is a uniformly distributed random variable that ranges from 6.9 to 11.9 pounds.

a. Calculate the expected value and standard deviation of this distribution. (Do not round intermediate calculations. Round your "expected value" to 2 decimal places and "standard deviation" answer to 4 decimal places.)

Expected value = ________ Standard deviation= _____________

b. Find the probability that the weight of a randomly selected bag is no more than 8.3 pounds. (Do not round intermediate calculations. Round your answer to 2 decimal place.)

Probability__________

c. Find the probability that the weight of a randomly selected bag is at least 7.4 pounds. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

Probability= _____________

1. A random variable X is exponentially distributed with an expected value of 36.

a-1.What is the rate parameter λ? (Round your answer to 3 decimal places.)

Rate parameter λ = ______________

a-2.What is the standard deviation of X?

Standard deviation = ____________

b. Compute P(29 ≤ X ≤ 43). (Round your intermediate calculations and final answer to 4 decimal places.)

P(29 ≤ X ≤ 43)=__________

c. Compute P(24 ≤ X ≤ 48). (Round your intermediate calculations and final answer to 4 decimal places.) P(24 ≤ X ≤ 48)= __________

2. The random variable X is normally distributed. Also, it is known that P(X > 186) = 0.03. Use Table 1. http://lectures.mhhe.com/connect/0073361615/Table/table1.jpg

a.Find the population mean μ, if the population standard deviation σ = 11. (Round "z" value to 2 decimal places and final answer to 2 decimal place.)

Mean=

b.Find the population mean μ, if the population standard deviation σ = 22. (Round "z" value to 2 decimal places and final answer to 2 decimal place.)

Mean =

c.Find the population standard deviation σ, if the population mean μ = 165. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

Standard deviation =

d.Find the population standard deviation σ, if the population mean μ = 153. (Round "z" value to 2 decimal places and final answer to 2 decimal places.)

Standard deviation =

3. The historical returns on a balanced portfolio have had an average return of 6% and a standard deviation of 8%. Assume that returns on this portfolio follow a normal distribution. Use the empirical rule to answer the following questions.

a.What percentage of returns were greater than 22%? (Round your answer to 2 decimal places.)

Percentage of returns_________ %

b. What percentage of returns were below −18%? (Round your answer to 2 decimal places.)

Percentage of returns__________ %

4. A random variable X follows the continuous uniform distribution with a lower bound of −7 and an upper bound of 14.

a. What is the height of the density function f(x)? (Round your answer to 4 decimal places.) f(x) =

b. What are the mean and the standard deviation of the distribution? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Mean =________ Standard deviation = ________

c. Calculate P(X ≤ −2). (Round your intermediate calculations and final answer to 4 decimal places.)

P(X ≤ −2)=

5. A random sample of size n = 241 is taken from a population of size N = 5,588 with mean μ = −68 and variance σ2 = 183. Use Table 1. http://lectures.mhhe.com/connect/0073361615/Table/table1.jpg

a-1. Calculate the expected value and the standard deviation of the sample mean. (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round "standard deviation" to 2 decimal places.) Expected value = -68 Standard deviation____________

b. What is the probability that the sample mean is between −70 and −66? (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability___________

c. What is the probability that the sample mean is greater than −67? (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability_______

6. A random sample of size n = 36 is taken from a population with mean μ = −6.8 and standard deviation σ = 3. Use Table 1.

b. What is the probability that the sample

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