Question 1

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed).What is the probability that the average price per square foot for a home is less than $108?

Accepted Answer

To find the probability that the average price per square foot is less than $108, we calculate the z-score: z = (108 - 100) / 5 = 1.6. Using the standard normal distribution table, the probability corresponding to a z-score of 1.6 is approximately 0.945.

Question 2

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses more than 580 minutes?

Accepted Answer

We need to find the probability that a student uses more than 580 minutes, which is equivalent to finding the area to the right of 580 on the normal distribution curve.

Using the Z-score formula:

z = (x - μ) / σ

Where:

x = 580 (the value we are interested in) 
μ = 500 (mean) 
σ = 50 (standard deviation)

z = (580 - 500) / 50 = 1.6

We can now find the area to the right of z = 1.6 using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we find that the area to the right of z = 1.6 is 0.0548.

Therefore, the probability that a student uses more than 580 minutes is 0.0548.

Question 3

The number of cars passing through an intersection in the next five minutes can usually be described by the

Accepted Answer

The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time, when those events occur independently and at a constant rate. In this case, the number of cars passing through an intersection could be modeled using a Poisson distribution, as the arrivals of cars are independent and random, with a constant average rate of arrival.

Question 4

Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour.What is the probability that in the next hour there will be exactly 12 arrivals?

Accepted Answer

The probability of exactly $k$ arrivals in a Poisson distribution is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean arrival rate and $k$ is the number of arrivals. Here, $\lambda = 16$ and $k = 12$. Plugging these values into the formula gives $P(X=12) = \frac{e^{-16} 16^{12}}{12!}$, which calculates to approximately 0.0661.

Question 5

Given a df₁ = 3 and df₂ = 6, what is the probability that F is greater than 4.3?

Accepted Answer

The probability that F is greater than 4.3 with df1 = 3 and df2 = 6 is 0.0610, based on the F-distribution table or calculation.

Question 6

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take less than 40 minutes?

Accepted Answer

Since the distribution is normal and symmetric, the mean (40 minutes) divides the distribution into two equal halves. Therefore, the probability of a time less than the mean (40 minutes) is 50%.

Question 7

Queuing Theory makes use of the

Accepted Answer

Queuing Theory uses the Poisson distribution to predict the arrival rate of customers, which is a fundamental component in designing efficient waiting lines.

Question 8

Which of the following statements concerning the F distribution is true?

Accepted Answer

The F distribution is not discrete and is not symmetrical. It is useful in testing hypotheses about variance, specifically in comparing the variances of two populations.

Question 9

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses between 400 and 500 minutes?

Accepted Answer

To find the probability that a student uses between 400 and 500 minutes, we calculate the z-scores for 400 and 500 minutes and then find the area under the normal distribution curve between these z-scores. The z-score formula is $z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For 400 minutes, $z = \frac{400 - 500}{50} = -2$, and for 500 minutes, $z = \frac{500 - 500}{50} = 0$. Looking up these z-scores in a standard normal distribution table or using a calculator, the area between $z = -2$ and $z = 0$ is approximately 0.4773, which corresponds to the probability of a student using between 400 and 500 minutes.

Question 10

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed).What is the probability that the average price per square foot for a home is less than $85?

Accepted Answer

To find the probability that the average price per square foot for a home is less than $85, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question ($85), μ is the mean ($100), and σ is the standard deviation ($5). Plugging in the values, we get Z = (85 - 100) / 5 = -15 / 5 = -3. Looking up a Z-score of -3 in a standard normal distribution table or using a calculator, we find the probability is approximately 0.0013, which rounds to 0.001, indicating a very low probability.

Question 11

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed).What is the probability that the average price per square foot for a home is greater than $90?

Accepted Answer

To find the probability that the average price per square foot for a home is greater than $90, we need to standardize the value using z-score formula:

z = (x - µ) / σ

where x is the value we want to standardize, µ is the mean, and σ is the standard deviation.

z = (90 - 100) / 5 = -2

Using a standard normal distribution table, we find that the probability of obtaining a z-score greater than -2 is approximately 0.977. Therefore, the probability that the average price per square foot for a home is greater than $90 is 0.977, or approximately 97.7%. The best choice is D.

Question 12

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take more than 40 minutes?

Accepted Answer

Since the distribution is normal and we are looking for the probability of a time greater than the mean (40 minutes), this corresponds to 50% of the distribution, as the mean divides a normal distribution into two equal halves.

Question 13

The number of calls received by call center follows a Poisson process with a rate of 1.5 per minute.What is the probability that a minute goes by without a call?

Accepted Answer

The Poisson distribution can be used to model the number of occurrences of a rare event in a fixed amount of time or space. In this case, the rare event is the call, and the distribution is Poisson with a rate of 1.5 calls per minute.

To find the probability that a minute goes by without a call, we can use the Poisson distribution formula:

P(X = 0) = (e^(-λ) * λ^x) / x!

where λ is the rate and x is the number of occurrences (in this case, 0).

Substituting in the values, we get:

P(X = 0) = (e^(-1.5) * 1.5^0) / 0! = e^(-1.5) ≈ 0.223

Therefore, the best choice is B, with a probability of approximately 0.223 that a minute goes by without a call.

Question 14

What is the probability that F is between 4 and 5, given a df₁ = 4 and df₂ = 6?

Accepted Answer

The probability that F is between 4 and 5 with degrees of freedom 4 and 6 can be found using the F-distribution tables or a calculator designed for statistical analysis. The exact value might not be directly available, but the probability of F falling between these values can be calculated by finding the cumulative probability up to F=5 and subtracting the cumulative probability up to F=4. The provided options suggest a specific calculation or approximation, and option C) 0.0248 is the correct choice based on typical F-distribution probabilities for these degrees of freedom.

Question 15

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take less than 35 minutes?

Accepted Answer

We need to find the probability that it will take less than 35 minutes to travel downtown.

Using the z-score formula: z = (x - mean) / standard deviation

z = (35 - 40) / 5 = -1

Using a standard normal distribution table, the probability of getting a z-score less than -1 is 0.15866.

Therefore, the probability that it will take less than 35 minutes is 0.15866 or 15.866%.

So, the best choice is B.

Question 16

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses more than 350 minutes?

Accepted Answer

To find the probability that a student uses more than 350 minutes, we need to find the area to the right of 350 under the normal curve. 
Using the z-score formula, we get:
z = (350-500)/50 = -3
Using a standard normal table, we can find that the probability of a z-score less than -3 (which is the same as the probability of a score greater than 350) is approximately 0.001. 
Therefore, the probability that a student uses more than 350 minutes is 0.001. 
So, the best choice is B.

Question 17

What is the F value associated with α = 0.05, numerator degrees of freedom (df₁)equal to 4, and denominator degrees of freedom (df₂)equal to 9?

Accepted Answer

The F value for α = 0.05, numerator degrees of freedom = 4, and denominator degrees of freedom = 9 is found in F-distribution tables or through statistical software. For these specific degrees of freedom, the F value is 3.63.

Question 18

The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks.The construction company must pay a penalty if the project is not finished by the due date in the contract.If a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date, what due date (project week #)should be negotiated?

Accepted Answer

To ensure a 90% chance of finishing on time, we need to find the z-score corresponding to the 90th percentile of a standard normal distribution, which is approximately 1.28. Using the formula for a value in a normal distribution, $X = \mu + Z\sigma$, where $\mu = 80$ weeks, $\sigma = 10$ weeks, and $Z = 1.28$, we calculate $X = 80 + 1.28(10) = 80 + 12.8 = 92.8$ weeks. This means the company should negotiate a due date of 92.8 weeks to be 90% sure of finishing on time.

Question 19

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed).What is the probability that the average price per square foot for a home is greater than $110?

Accepted Answer

We can use the z-score formula to calculate the probability:
z = (110 - 100) / 5 = 2
Using a standard normal distribution table, the probability of getting a z-score greater than 2 is 0.023. Therefore, the probability that the average price per square foot for a home is greater than $110 is 0.023 or 2.3%.

Question 20

The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks.The construction company must pay a penalty if the project is not finished by the due date in the contract.If a construction company bidding on this contract puts in a due date of 80 weeks, what is the probability that they will have to pay a penalty?

Accepted Answer

If the due date is set at 80 weeks and the project takes longer, the company will have to pay a penalty. From the given information, we know that the mean completion time is 80 weeks and the standard deviation is 10 weeks. We can use these values to calculate the z-score for the due date of 80 weeks:

z = (80 - 80) / 10 = 0

Since we are looking for the probability of the project taking longer than 80 weeks (resulting in a penalty), we need to find the area to the right of the z-score of 0 on a standard normal distribution table. This area is 0.500 or 50%.

Therefore, the probability of the company having to pay a penalty is 0.500 or 50%.

Quiz 2: Probability Concepts and Applications

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed) .What is the probability that the average price per square foot for a home is less than $108?

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses more than 580 minutes?

The number of cars passing through an intersection in the next five minutes can usually be described by the

Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour.What is the probability that in the next hour there will be exactly 12 arrivals?

Given a df₁ = 3 and df₂ = 6, what is the probability that F is greater than 4.3?

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take less than 40 minutes?

Queuing Theory makes use of the

Which of the following statements concerning the F distribution is true?

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses between 400 and 500 minutes?

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed) .What is the probability that the average price per square foot for a home is less than $85?

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed) .What is the probability that the average price per square foot for a home is greater than $90?

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take more than 40 minutes?

The number of calls received by call center follows a Poisson process with a rate of 1.5 per minute.What is the probability that a minute goes by without a call?

What is the probability that F is between 4 and 5, given a df₁ = 4 and df₂ = 6?

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take less than 35 minutes?

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses more than 350 minutes?

What is the F value associated with α = 0.05, numerator degrees of freedom (df₁) equal to 4, and denominator degrees of freedom (df₂) equal to 9?

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed) .What is the probability that the average price per square foot for a home is greater than $110?

Quiz 2: Probability Concepts and Applications

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed) .What is the probability that the average price per square foot for a home is less than $108?

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses more than 580 minutes?

The number of cars passing through an intersection in the next five minutes can usually be described by the

Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour.What is the probability that in the next hour there will be exactly 12 arrivals?

Given a df1 = 3 and df2 = 6, what is the probability that F is greater than 4.3?

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take less than 40 minutes?

Queuing Theory makes use of the

Which of the following statements concerning the F distribution is true?

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses between 400 and 500 minutes?

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed) .What is the probability that the average price per square foot for a home is less than $85?

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed) .What is the probability that the average price per square foot for a home is greater than $90?

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take more than 40 minutes?

The number of calls received by call center follows a Poisson process with a rate of 1.5 per minute.What is the probability that a minute goes by without a call?

What is the probability that F is between 4 and 5, given a df1 = 4 and df2 = 6?

The time required to travel downtown at 10 a.m.on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes.What is the probability that it will take less than 35 minutes?

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50.What is the probability that a student uses more than 350 minutes?

What is the F value associated with α = 0.05, numerator degrees of freedom (df1) equal to 4, and denominator degrees of freedom (df2) equal to 9?

Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed) .What is the probability that the average price per square foot for a home is greater than $110?

Given a df₁ = 3 and df₂ = 6, what is the probability that F is greater than 4.3?

What is the probability that F is between 4 and 5, given a df₁ = 4 and df₂ = 6?

What is the F value associated with α = 0.05, numerator degrees of freedom (df₁) equal to 4, and denominator degrees of freedom (df₂) equal to 9?