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Exam 8: Continuous Probability Distributions

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Question 41

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In the standard normal distribution, z_0.05 = 1.645 means that 5% of all values of z are below 1.645 and 95% are above it.

A) True
B) False

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Question 42

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If the mean of an exponential distribution is 2, then the value of the parameter $\lambda$ is 2.0.

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B) False

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Question 43

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As the degrees of freedom approach infinity, the values of a Student t distribution approach those of a standard normal distribution.

Counter Sales Suppose that customers arrive at a counter at an average rate of three customers per minute and that their arrivals follow the Poisson model. -{Counter Sales Narrative} Use the appropriate exponential distribution to find the probability that the next customer will not arrive within the next 2 minutes.

A(n) ____________________ random variable is one that assumes an uncountable number of possible values.

Which of the following statements is true?

Counter Sales Suppose that customers arrive at a counter at an average rate of three customers per minute and that their arrivals follow the Poisson model. -{Counter Sales Narrative} Write the probability density function of the distribution of the time that will elapse before the next customer arrives.

Which of the following does not represent a continuous uniform random variable?

If Z is a standard normal random variable, find the following probabilities: a. P(Z $\le$ -1.77) b. P(Z $\le$ -1.96) c. P(0.35 $\le$ Z $\le$ 0.85) d. P(-2.88 $\le$ Z $\le$ -2.15) e. P(Z $\le$ 1.45)

The F distribution has two parameters called degrees of freedom, ₁ and 11ef1783_5b2f_5d45_8934_51a7cec6335a_TB7453_11₂.We call 11ef1783_5b2f_5d45_8934_51a7cec6335a_TB7453_11₁ the ____________________ degrees of freedom, and we call 11ef1783_5b2f_5d45_8934_51a7cec6335a_TB7453_11₂ the ____________________ degrees of freedom.

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

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?

A continuous random variable X has the following probability density function: f(x) = 1/4, 0 $\le$ x $\le$ 4 Find the following probabilities: a. P(X $\le$ 1) b. P(X $\ge$ 2) c. P(1 $\le$ X $\le$ 2) d. P(X = 3)

A continuous random variable is one that can assume an uncountable number of values.

A probability density function shows the probability for each value of X.

Suppose f(x) = 0.25.What range of possible values can X take on and still have the density function be legitimate?

Suppose X is a normal random variable with mean 70 and standard deviation 3.Then P(X = 3) = ____________________.

Which of the following distributions can take on negative values?

Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.5.What proportions of the values of X are: a. less than 14 b. more than 8 c. between 10 and 13

Use the F table to find the following values of F. a. F_.99,12,20 b. F_.95,20,40 c. F_.975,5,15 d. F_.99,8,30