Exam 8: Continuous Probability Distributions

Diet Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds. -{Diet Narrative} If a dieter is selected at random,what is the probability that the dieter lost more than 7.5 pounds?

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Question 1

Correct Answer:

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0.6915

Which of the following has a mean and variance that depend on degrees of freedom?

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(Multiple Choice)

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Question 2

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Let X be an exponential random variable with λ = 1.50.Find the following: a.P(X ≥ 2) b.P(X ≤ 4) c.P(1 ≤ X ≤ 3) d.P(X = 1)

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Question 3

Correct Answer:

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a. 0.0498 (note that f(x)= 1.50e−1.50x for x ≥ 0)
b. 0.9975
c. 0.2120
d. 0

Checking Accounts A bank has determined that the monthly balances of the checking accounts of its customers are normally distributed with an average balance of $1,200 and a standard deviation of $250. -{Checking Accounts Narrative} What proportion of customers have monthly balances more than $1,125?

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Question 4

You can use a continuous random variable to ____________________ a discrete random variable that takes on a countable,but very large,number of possible values.

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Question 5

The probability density function f(x)for a uniform random variable X defined over the interval [2,10] is

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Question 6

Most values of a standard normal distribution lie between:

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Question 7

If we standardize the normal curve,we express the original X values in terms of their number of standard deviations away from the mean.

(True/False)

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Question 8

IT Graduates Salary The recent average starting salary for new college graduates in IT systems is $47,500.Assume salaries are normally distributed with a standard deviation of $4,500. -{IT Graduates Salary Narrative} What is the cutoff for the top 3% of the salaries?

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Question 9

P(Z < 3.00)is approximately ____________________.

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Question 10

We define as the value of the F with v₁ and v₂ degrees of freedom such that the area to its right under the F curve is A,while is defined as the value such that the area to its left is A.

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Question 11

The Student t distribution:

(Multiple Choice)

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Question 12

The value of an F distribution with v₁ = 5 and v₂ = 10 degrees of freedom such that the area to its left is 0.95 is 3.33.

(True/False)

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Question 13

The mean of a Student t distribution is ____________________.

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Question 14

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. -{Waiting Time Narrative} What is the probability that a patient would have to wait no more than one hour?

(Short Answer)

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Question 15

Like that of the Student t distribution,the shape of the chi-squared distribution depends on its number of degrees of freedom.

(True/False)

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Question 16

Since there is an infinite number of values a continuous random variable can assume,the probability of each individual value is virtually 0.

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Question 17

Which of the following distributions can take on negative values?

(Multiple Choice)

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Question 18

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. -{Battery Life Narrative} What proportion of these batteries will last between 3,800 and 4,100 hours?

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Question 19

Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes. -{Repair Time Narrative} What is the probability that it will take a technician between 10 to 15 minutes to fix a telephone problem?

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Question 20

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Exam 8: Continuous Probability Distributions

Which of the following has a mean and variance that depend on degrees of freedom?

Let X be an exponential random variable with λ = 1.50.Find the following: a.P(X ≥ 2) b.P(X ≤ 4) c.P(1 ≤ X ≤ 3) d.P(X = 1)

You can use a continuous random variable to ____________________ a discrete random variable that takes on a countable,but very large,number of possible values.

The probability density function f(x)for a uniform random variable X defined over the interval [2,10] is

Most values of a standard normal distribution lie between:

If we standardize the normal curve,we express the original X values in terms of their number of standard deviations away from the mean.

IT Graduates Salary The recent average starting salary for new college graduates in IT systems is $47,500.Assume salaries are normally distributed with a standard deviation of $4,500. ​ ​ -{IT Graduates Salary Narrative} What is the cutoff for the top 3% of the salaries?

P(Z < 3.00)is approximately ____________________.

We define as the value of the F with v1 and v2 degrees of freedom such that the area to its right under the F curve is A,while is defined as the value such that the area to its left is A.

The Student t distribution:

The value of an F distribution with v1 = 5 and v2 = 10 degrees of freedom such that the area to its left is 0.95 is 3.33.

The mean of a Student t distribution is ____________________.

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. ​ ​ -{Waiting Time Narrative} What is the probability that a patient would have to wait no more than one hour?

Like that of the Student t distribution,the shape of the chi-squared distribution depends on its number of degrees of freedom.

Since there is an infinite number of values a continuous random variable can assume,the probability of each individual value is virtually 0.

Which of the following distributions can take on negative values?

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. ​ ​ -{Battery Life Narrative} What proportion of these batteries will last between 3,800 and 4,100 hours?

Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes. ​ ​ -{Repair Time Narrative} What is the probability that it will take a technician between 10 to 15 minutes to fix a telephone problem?

What Is Statistics

Graphical Descriptive Techniques 1

Graphical Descriptive Techniques 2

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analytics and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

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IT Graduates Salary The recent average starting salary for new college graduates in IT systems is $47,500.Assume salaries are normally distributed with a standard deviation of $4,500. -{IT Graduates Salary Narrative} What is the cutoff for the top 3% of the salaries?

We define as the value of the F with v₁ and v₂ degrees of freedom such that the area to its right under the F curve is A,while is defined as the value such that the area to its left is A.

The value of an F distribution with v₁ = 5 and v₂ = 10 degrees of freedom such that the area to its left is 0.95 is 3.33.

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. -{Waiting Time Narrative} What is the probability that a patient would have to wait no more than one hour?

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. -{Battery Life Narrative} What proportion of these batteries will last between 3,800 and 4,100 hours?

Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes. -{Repair Time Narrative} What is the probability that it will take a technician between 10 to 15 minutes to fix a telephone problem?