If x is uniformly distributed over some interval. The mean value (μ) of x is 2 and its variance (σ2) is 1/3. The probability that x is between 2 and 2.5, P(2 $\le$ x $\le$ 2.5), is ___.

A) 0.45 B) 0.40 C) 0.35 D) 0.33 E) 0.25 A) 0.45 B) 0.40 C) 0.35 D) 0.33 E) 0.25

Exam 8: Continuous Distributions

If x is uniformly distributed over some interval. The mean value (μ) of x is 2 and its variance (σ²) is 1/3. The probability that x is between 2 and 2.5, P(2 $\le$ x $\le$ 2.5), is ___.

(Multiple Choice)

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Question 21

Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > 2.4)?

(Multiple Choice)

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Question 22

If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the height of this distribution, f(x), is ___.

(Multiple Choice)

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Question 23

If x is continuously uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the probability, P(9 $\le$ x $\le$ 11) is ___.

(Multiple Choice)

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Question 24

Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life of at least 50,000 miles?

(Multiple Choice)

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Question 25

The net profit from a certain investment is normally distributed with a mean of $2,500 and a standard deviation of $1,000. The probability that the investor's net gain will be at least $2,000 is ___.

(Multiple Choice)

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Question 26

The height of the rectangle depicting a uniform distribution is the probability of each outcome and it same for all of the possible outcomes.

(True/False)

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Question 27

If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the probability that an oil change job is completed in 21.75 to 24.25 minutes, inclusively, i.e., P(21.75 $\le$ x $\le$ 24.25) is ___.

(Multiple Choice)

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Question 28

A z score is the number of ___ that a value is from the mean.

(Multiple Choice)

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Question 29

Suppose the mean time to fill a routine prescription at a local pharmacy is 35 minutes based on the time the physician places the order to the time it is dispensed. Assume the standard deviation is 11 minutes. The z score for x = 46 is ___.

(Multiple Choice)

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Question 30

Sure Stone Tire Company has established that the useful life of a particular brand of its automobile tires is normally distributed with a mean of 40,000 miles and a standard deviation of 5000 miles. What is the probability that a randomly selected tire of this brand has a life between 30,000 and 50,000 miles?

(Multiple Choice)

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Question 31

The area under the standard normal distribution between 0 and 2 is twice the area between 0 and 1.

(True/False)

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Question 32

A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years. If the random variable x = Age is normally distributed, a) What is the probability that a student will be younger than 16.2 years? b) How many students are older than 16.2 years?

(Short Answer)

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Question 33

The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 1100 hours?

(Multiple Choice)

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Question 34

A standard normal distribution has a mean of one and a standard deviation of three.

(True/False)

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Question 35

Let z be a normal random variable with mean 0 and standard deviation 1. The 90^th percentile of z is ___.

(Multiple Choice)

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Question 36

A standard normal distribution has the following characteristics:

(Multiple Choice)

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Question 37

A normal distribution with a mean of zero and a standard deviation of 1 is called a null distribution.

(True/False)

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Question 38

If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the probability that an oil change job is completed in 33 to 35 minutes, inclusively, i.e., P(33 $\le$ x $\le$ 35) is ___.

(Multiple Choice)

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Question 39

If x, the time (in minutes) to complete an change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the probability that an oil change job is completed in 25 to 28 minutes, inclusively, i.e., P(25 $\le$ x $\le$ 28) is ___.

(Multiple Choice)

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Question 40

Showing 21 - 40 of 64

If x is uniformly distributed over some interval. The mean value (μ) of x is 2 and its variance (σ²) is 1/3. The probability that x is between 2 and 2.5, P(2 $\le$ x $\le$ 2.5), is ___.

Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > 2.4)?

If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the height of this distribution, f(x), is ___.

If x is continuously uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the probability, P(9 $\le$ x $\le$ 11) is ___.

The net profit from a certain investment is normally distributed with a mean of $2,500 and a standard deviation of $1,000. The probability that the investor's net gain will be at least $2,000 is ___.

The height of the rectangle depicting a uniform distribution is the probability of each outcome and it same for all of the possible outcomes.

A z score is the number of ___ that a value is from the mean.

Suppose the mean time to fill a routine prescription at a local pharmacy is 35 minutes based on the time the physician places the order to the time it is dispensed. Assume the standard deviation is 11 minutes. The z score for x = 46 is ___.

The area under the standard normal distribution between 0 and 2 is twice the area between 0 and 1.

A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years. If the random variable x = Age is normally distributed, a) What is the probability that a student will be younger than 16.2 years? b) How many students are older than 16.2 years?

The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 1100 hours?

A standard normal distribution has a mean of one and a standard deviation of three.

Let z be a normal random variable with mean 0 and standard deviation 1. The 90^th percentile of z is ___.

A standard normal distribution has the following characteristics:

A normal distribution with a mean of zero and a standard deviation of 1 is called a null distribution.

Introduction to Statistics

Organizing and Visualizing Data

Descriptive Statistics

Gathering Data

Probability

Decision Analysis and Expected Value

Discrete Probability Distributions

Sampling Distributions

Confidence Intervals

Hypothesis Testing for Single Populations

Hypothesis Testing for Two Populations

Analysis of Variance Anova

Linear Correlation and Simple Linear Regression Analysis

Categorical Versus Categorical: Tests

Filters

Exam 8: Continuous Distributions

If x is uniformly distributed over some interval. The mean value (μ) of x is 2 and its variance (σ2) is 1/3. The probability that x is between 2 and 2.5, P(2 ≤\le≤ x ≤\le≤ 2.5), is ___.

Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > 2.4)?

If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 ≤\le≤ x ≤\le≤ 30), then the height of this distribution, f(x), is ___.

If x is continuously uniformly distributed over the interval 8 to 12, inclusively (8 ≤\le≤ x ≤\le≤ 12), then the probability, P(9 ≤\le≤ x ≤\le≤ 11) is ___.

The net profit from a certain investment is normally distributed with a mean of $2,500 and a standard deviation of $1,000. The probability that the investor's net gain will be at least $2,000 is ___.

The height of the rectangle depicting a uniform distribution is the probability of each outcome and it same for all of the possible outcomes.

A z score is the number of ___ that a value is from the mean.

Suppose the mean time to fill a routine prescription at a local pharmacy is 35 minutes based on the time the physician places the order to the time it is dispensed. Assume the standard deviation is 11 minutes. The z score for x = 46 is ___.

The area under the standard normal distribution between 0 and 2 is twice the area between 0 and 1.

A group of 625 students has a mean age of 15.8 years with a standard deviation of 0.6 years. If the random variable x = Age is normally distributed, a) What is the probability that a student will be younger than 16.2 years? b) How many students are older than 16.2 years?

The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 1100 hours?

A standard normal distribution has a mean of one and a standard deviation of three.

Let z be a normal random variable with mean 0 and standard deviation 1. The 90th percentile of z is ___.

A standard normal distribution has the following characteristics:

A normal distribution with a mean of zero and a standard deviation of 1 is called a null distribution.

Introduction to Statistics

Organizing and Visualizing Data

Descriptive Statistics

Gathering Data

Probability

Decision Analysis and Expected Value

Discrete Probability Distributions

Sampling Distributions

Confidence Intervals

Hypothesis Testing for Single Populations

Hypothesis Testing for Two Populations

Analysis of Variance Anova

Linear Correlation and Simple Linear Regression Analysis

Categorical Versus Categorical: Tests

Filters

If x is uniformly distributed over some interval. The mean value (μ) of x is 2 and its variance (σ²) is 1/3. The probability that x is between 2 and 2.5, P(2 $\le$ x $\le$ 2.5), is ___.

If x, the time (in minutes) to complete an oil change job at certain auto service station, is uniformly distributed over the interval 20 to 30, inclusively (20 $\le$ x $\le$ 30), then the height of this distribution, f(x), is ___.

If x is continuously uniformly distributed over the interval 8 to 12, inclusively (8 $\le$ x $\le$ 12), then the probability, P(9 $\le$ x $\le$ 11) is ___.

Let z be a normal random variable with mean 0 and standard deviation 1. The 90^th percentile of z is ___.