Exam 5: Continuous Random Variables

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. -What is the probability of getting a grade of 91 or less on this exam?

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Question 1

Correct Answer:

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.9927
P(x ≤ 91)= p(z ≤ (91 - 69)/9)= p(z ≤ 2.44),.5000 + .4927)= .9927

An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed. -What proportion of tests has scores over 90?

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Question 2

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.0228 $\begin{array} { l } Z = \frac { 90 - 80 } { 5 } = 2 \\P ( X > 90 ) = .5 - .4772 = .0228\end{array}$

If x is a binomial random variable where n = 100 and p = .2,find the probability that x is less than or equal to 18 using the normal approximation to the binomial.

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Question 3

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.5675 $P ( X \leq 18 ) \stackrel { c c } { = } P ( X \leq 18.5 ) = P \left( Z \leq \frac { 18.5 - 20 } { \sqrt { 16 } } \right) \approx P ( Z \leq - 0.38 ) = 0.3520$

Find z when the area between 0 and z is .4750

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Question 4

All continuous random variables are normally distributed.

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Question 5

A company must decide their contribution to their pension plan based on the probability distribution of the length of life of their retired employees. Suppose the probability distribution of the lifetimes of their employees is approximately a normal distribution with μ = 74 years and σ = 8.6 years. -What percentage of their retired employees would receive payments beyond age 76?

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Question 6

Between what two values (in dollars)symmetrically distributed around the population mean will 80% of the drink prices fall?

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Question 7

The weight of a product is normally distributed with a standard deviation of 0.5 grams.If the production manager wants no more than 5% of the products to weigh more than 5.1 grams,then the average weight should be _____.

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Question 8

The weight of a product is normally distributed with a mean of four grams and a variance of .25 "squared grams." What is the probability that a randomly selected unit from a recently manufactured batch weighs: -The weight of a product is normally distributed with a standard deviation of .5 grams.What should the average weight be if the production manager wants no more than 5% of the products to weigh more than 5.1 grams?

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Question 9

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard of 20. -A movie theatre manager knows that the number of patrons per movie is normally distributed with a mean of 200 and a standard deviation of 20.What is the number of patrons,x,where 50% are less than x?

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Question 10

If the wages of workers for a given company are normally distributed with a mean of $15 per hour,then the proportion of the workers earning more than $13 per hour:

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Question 11

The average time a subscriber spends reading the local newspaper is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed. -What is the probability a subscriber will spend no more than 30 minutes reading the paper?

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Question 12

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. -What is the expected value of the water depth?

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Question 13

The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime: -The time between breakdowns of an alarm system is exponentially distributed with mean 10 days.What is the probability that there are no breakdowns on a given day?

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Question 14

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard of 20. -What percentage of the time will the number of boxes received weekly be greater than 210 or less than 180?

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Question 15

The thickness of randomly selected metal piece is a ___________ random variable.

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Question 16

If the random variable of x is normally distributed,68.26% of all possible observed values of x will be within two standard deviations of the mean.

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Question 17

A continuous random variable may assume only integer values in a given interval.

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Question 18

The temperature for the month of July with the humidex factor is normally distributed with a mean of 30.05°C with a standard deviation of 0.2°C. -What is the probability that a daily July temperature taken at random from the population is between 29.75C and 30.5C?

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Question 19

The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.

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Question 20

Showing 1 - 20 of 167

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9. -What is the probability of getting a grade of 91 or less on this exam?

An aptitude test has a mean score of 80 and a standard deviation of 5. The population of scores is normally distributed. -What proportion of tests has scores over 90?

If x is a binomial random variable where n = 100 and p = .2,find the probability that x is less than or equal to 18 using the normal approximation to the binomial.

Find z when the area between 0 and z is .4750

All continuous random variables are normally distributed.

Between what two values (in dollars)symmetrically distributed around the population mean will 80% of the drink prices fall?

The weight of a product is normally distributed with a standard deviation of 0.5 grams.If the production manager wants no more than 5% of the products to weigh more than 5.1 grams,then the average weight should be _____.

If the wages of workers for a given company are normally distributed with a mean of $15 per hour,then the proportion of the workers earning more than $13 per hour:

The average time a subscriber spends reading the local newspaper is 49 minutes. Assume the standard deviation is 16 minutes and that the times are normally distributed. -What is the probability a subscriber will spend no more than 30 minutes reading the paper?

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. -What is the expected value of the water depth?

The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime: -The time between breakdowns of an alarm system is exponentially distributed with mean 10 days.What is the probability that there are no breakdowns on a given day?

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard of 20. -What percentage of the time will the number of boxes received weekly be greater than 210 or less than 180?

The thickness of randomly selected metal piece is a ___________ random variable.

If the random variable of x is normally distributed,68.26% of all possible observed values of x will be within two standard deviations of the mean.

A continuous random variable may assume only integer values in a given interval.

The temperature for the month of July with the humidex factor is normally distributed with a mean of 30.05°C with a standard deviation of 0.2°C. -What is the probability that a daily July temperature taken at random from the population is between 29.75C and 30.5C?

The area under the normal curve between z = 0 and z = 1 is ________________ the area under the normal curve between z = 1 and z = 2.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

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