What proportion of the data from a normal distribution is within 2 standard deviations of the mean? $\begin{array}{|l|l|} \hline\text { A. } & 0.3413 . \\ \hline \text { B. } & 0.4772 . \\ \hline \text { C. } & 0.6826 . \\ \hline \text { D. } & 0.9544 . \\ \hline \end{array}$

The answer of What proportion of the data from a...

If the random variable X is exponentially distributed with parameter $\lambda$ = 4, then the probability P(X $\leq$ 0.25), up to 4 decimal places, is: $\begin{array}{|l|l|} \hline A&\text { 0.6321}\\ \hline B&\text { 0.3679}\\ \hline C&\text { 0.2500}\\ \hline D&\text { None of these choices are correct.}\\ \hline \end{array}$

The answer of If the random variable X is exponentially...

Given that Z is a standard normal variable, the value z for which P(Z $\leq$ z) = 0.6736 is: $\begin{array}{|l|l|} \hline\text { A. } & 0.1736 . \\ \hline \text { B. } & 0.45 . \\ \hline \text { C. } & -0.1736 . \\ \hline \text { D. } & -0.45 . \\ \hline \end{array}$

The answer of Given that Z is a standard normal...

The probability density function, f(x), for any continuous random variable X, represents: $\begin{array}{|l|l|} \hline A&\text {all possible values that \( X $ will assume within some interval $ a \leq x \leq b $. }\\ \hline B&\text {the probability that $ X $ takes on a specific value $ x $ }\\ \hline C&\text { the area under the curve at $ x $.}\\ \hline D&\text { the height of the function at $ x $.}\\ \hline \end{array}\)

The answer of The probability density function, f(x), for any...

The probability density function f(x) of a random variable X that is uniformly distributed between a and b is: $\begin{array}{|l|l|} \hline\text { A. } & 1 /(b-a) . \\ \hline \text { B. } & 1 /(a-b) \\ \hline \text { C. } & (b-a) / 2 \\ \hline \text { D. } & (a-b) / 2 . \\ \hline \end{array}$

The answer of The probability density function f(x) of a...

The expected value, E(X), of a uniform random variable X defined over the interval $a \leq x \leq b$ , is: $\begin{array}{|l|l|} \hline\text { A. } & a+b \\ \hline \text { B. } & a-b \\ \hline \text { C. } & (a+b) / 2 \\ \hline \text { D. } & (a-b) / 2 \\ \hline \end{array}$

The answer of The expected value, E(X), of a uniform...

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter? $\begin{array}{|l|l|} \hline\text { A. } & \text { Uni form. } \\ \hline \text { B. } & \text { Normal. } \\ \hline \text { C. } & \text { Exponential. } \\ \hline \text { D. } & \text { Poisson. } \\ \hline \end{array}$

The answer of Which of the following distributions is appropriate...

Exam 8: Continuous Probability Distributions

Suppose that the probability p of a success on any trial of a binomial distribution equals 0.80. For which value of the number of trials, n, would the normal distribution provide a good approximation to the binomial distribution? A. 25. B. 20. C. 10. D. 15.

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Question 1

Correct Answer:

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A

In the normal distribution, the curve is asymptotic but never intercepts the horizontal axis either to the left or right.

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Question 2

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True

If the random variable X is exponentially distributed, then which of the following statements best describes the mean of X? $\begin{array}{|l|l|}\hline A&\text { The mean of \mathrm{X} will be greater than the standard deviation of $ \mathrm{X} $. }\\\hline B&\text { The mean of $ \mathrm{X} $ will be smaller than the standard deviation of $ \mathrm{X} $. }\\\hline C&\text {The mean of $ \mathrm{X} $ will equal the standard deviation of $ \mathrm{X} $. }\\\hline D&\text {None of these choices are correct. }\\\hline \end{array}$

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Question 3

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C

What proportion of the data from a normal distribution is within 2 standard deviations of the mean? A. 0.3413. B. 0.4772. C. 0.6826. D. 0.9544.

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Question 4

If the random variable X is exponentially distributed with parameter $\lambda$ = 4, then the probability P(X $\leq$ 0.25), up to 4 decimal places, is: A 0.6321 B 0.3679 C 0.2500 D None of these choices are correct.

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Question 5

Given that Z is a standard normal variable, the value z for which P(Z $\leq$ z) = 0.6736 is: A. 0.1736. B. 0.45. C. -0.1736. D. -0.45.

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Question 6

The probability density function, f(x), for any continuous random variable X, represents: A all possible values that X will assume within some interval a\leqx\leqb . B the probability that X takes on a specific value x C the area under the curve at x . D the height of the function at x .

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Question 7

The scores of high-school students sitting a mathematics exam were normally distributed, with a mean of 86 and a standard deviation of 4. a. What is the probability that a randomly selected student will have a score of 80 or less? b. If there were 97 680 students with scores higher than 91, how many students took the test?

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Question 8

In the normal distribution, the curve is skewed.

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Question 9

Using the standard normal curve, the z-score representing the 10th percentile is 1.28.

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Question 10

The probability density function f(x) of a random variable X that is uniformly distributed between a and b is: A. 1/(b-a). B. 1/(a-b) C. (b-a)/2 D. (a-b)/2.

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Question 11

If the random variable X is exponentially distributed and the parameter of the distribution $\lambda$ = 4, then P(X $\le$ 0.25) = 0.3679.

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Question 12

The expected value, E(X), of a uniform random variable X defined over the interval $a \leq x \leq b$ , is: A. a+b B. a-b C. (a+b)/2 D. (a-b)/2

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Question 13

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

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Question 14

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter? A. Uni form. B. Normal. C. Exponential. D. Poisson.

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Question 15

The lifetime of a light bulb is exponentially distributed with $\lambda$ = 0.001. a. What are the mean and standard deviation of the light bulb's lifetime? b. Find the probability that a light bulb will last between 110 and 150 hours. c. Find the probability that a light bulb will last for more than 125 hours.

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Question 16

A continuous random variable X has the probability density function f(x) = 2 $e ^ { - 2 x }$ , x $\ge$ 0. a. Find the mean and standard deviation of X. b. What is the probability that X is between 1 and 3? c. What is the probability that X is at most 2?

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Question 17

The values of z_A are the 100(1 - A)th percentiles of a standard normal random variable.

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Question 18

Which of the following is not true for an exponential distribution with parameter $\lambda$ ? A \mu=1/\lambda B \sigma=1/\lambda C The distribution is completely determined once the value of \lambda is known. D The distribution is a two-parameter distribution, since the mean and standard deviation are equal.

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Question 19

The mean and standard deviation of a normally distributed random variable that has been standardised are one and zero, respectively.

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Question 20

Exam 8: Continuous Probability Distributions

Suppose that the probability p of a success on any trial of a binomial distribution equals 0.80. For which value of the number of trials, n, would the normal distribution provide a good approximation to the binomial distribution? A. 25. B. 20. C. 10. D. 15.

In the normal distribution, the curve is asymptotic but never intercepts the horizontal axis either to the left or right.

What proportion of the data from a normal distribution is within 2 standard deviations of the mean? A. 0.3413. B. 0.4772. C. 0.6826. D. 0.9544.

If the random variable X is exponentially distributed with parameter λ\lambdaλ = 4, then the probability P(X ≤\leq≤ 0.25), up to 4 decimal places, is: A 0.6321 B 0.3679 C 0.2500 D None of these choices are correct.

Given that Z is a standard normal variable, the value z for which P(Z ≤\leq≤ z) = 0.6736 is: A. 0.1736. B. 0.45. C. -0.1736. D. -0.45.

The probability density function, f(x), for any continuous random variable X, represents: A all possible values that X will assume within some interval a\leqx\leqb . B the probability that X takes on a specific value x C the area under the curve at x . D the height of the function at x .

In the normal distribution, the curve is skewed.

Using the standard normal curve, the z-score representing the 10th percentile is 1.28.

The probability density function f(x) of a random variable X that is uniformly distributed between a and b is: A. 1/(b-a). B. 1/(a-b) C. (b-a)/2 D. (a-b)/2.

If the random variable X is exponentially distributed and the parameter of the distribution λ\lambdaλ = 4, then P(X ≤\le≤ 0.25) = 0.3679.

The expected value, E(X), of a uniform random variable X defined over the interval a≤x≤ba \leq x \leq ba≤x≤b , is: A. a+b B. a-b C. (a+b)/2 D. (a-b)/2

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

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter? A. Uni form. B. Normal. C. Exponential. D. Poisson.

A continuous random variable X has the probability density function f(x) = 2 e−2xe ^ { - 2 x }e−2x , x ≥\ge≥ 0. a. Find the mean and standard deviation of X. b. What is the probability that X is between 1 and 3? c. What is the probability that X is at most 2?

The values of zA are the 100(1 - A)th percentiles of a standard normal random variable.

The mean and standard deviation of a normally distributed random variable that has been standardised are one and zero, respectively.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

If the random variable X is exponentially distributed with parameter $\lambda$ = 4, then the probability P(X $\leq$ 0.25), up to 4 decimal places, is: A 0.6321 B 0.3679 C 0.2500 D None of these choices are correct.

Given that Z is a standard normal variable, the value z for which P(Z $\leq$ z) = 0.6736 is: A. 0.1736. B. 0.45. C. -0.1736. D. -0.45.

If the random variable X is exponentially distributed and the parameter of the distribution $\lambda$ = 4, then P(X $\le$ 0.25) = 0.3679.

The expected value, E(X), of a uniform random variable X defined over the interval $a \leq x \leq b$ , is: A. a+b B. a-b C. (a+b)/2 D. (a-b)/2

A continuous random variable X has the probability density function f(x) = 2 $e ^ { - 2 x }$ , x $\ge$ 0. a. Find the mean and standard deviation of X. b. What is the probability that X is between 1 and 3? c. What is the probability that X is at most 2?

The values of z_A are the 100(1 - A)th percentiles of a standard normal random variable.