Question 1

Exceeds 3 minutes?

Accepted Answer

3012 exceeds 3 minutes, as 3 minutes is equal to 180 seconds, and 3012 is greater than 180.

Question 2

A normal population has a mean of 10 and a variance of 4.What is P(X > 7)?

Accepted Answer

The answer of A normal population has a mean of...

Question 3

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 less than 160?

Accepted Answer

To find the percentage of time the number of boxes received weekly is less than 160, we calculate the Z-score using the formula Z = (X - μ) / σ, where X is the value in question (160), μ is the mean (200), and σ is the standard deviation (20). Plugging in the values, we get Z = (160 - 200) / 20 = -40 / 20 = -2. A Z-score of -2 corresponds to a percentile of approximately 2.28% in the standard normal distribution, which means about 2.28% of the time, the number of boxes received will be less than 160.

Question 4

Suppose the distribution of integrity test scores is normally distributed with a mean of 15 and a variance of 25.Using this information,what percentage of the population scores greater than 15?

Accepted Answer

Since the mean is 15 and the distribution is normal, we know that exactly 50% of the population will score greater than 15. Therefore, choice D is the best answer.

Question 5

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 between 180 and 210?

Accepted Answer

The z-score for 180 is (180-200)/20 = -1. The z-score for 210 is (210-200)/20 = 0.5. The area under the normal curve between z-scores of -1 and 0.5 is 0.5328.

Question 6

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?

Accepted Answer

The answer of A plant manager knows that the number...

Question 7

A normal population has a mean of 10 and a variance of 4.What is P(X < 6)?

Accepted Answer

To find P(X < 6), we first calculate the Z-score: Z = (X - mean) / standard deviation = (6 - 10) / sqrt(4) = -2. The Z-score of -2 corresponds to a probability of 0.0228 in the standard normal distribution table.

Question 8

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 80% are less than x?

Accepted Answer

To find the number of patrons, x, where 80% are less than x, we need to find the z-score that corresponds to the 80th percentile.

Using a standard normal distribution table, we can find that the z-score for the 80th percentile is approximately 0.84.

We can then use the formula:

z = (x - μ) / σ

where z is the z-score, μ is the mean, and σ is the standard deviation.

Plugging in the values we know:

0.84 = (x - 200) / 20

Solving for x:

x - 200 = 0.84 * 20

x - 200 = 16.8

x = 216.8

Therefore, the answer is A) 216.8.

Question 9

The distance between store outlets in a chain of stores in a large metropolitan city is normally distributed with an average of 50km and a standard deviation of 5km.What is the probability of finding a store no less than 55km away?

Accepted Answer

The Z-score for 55km is (55-50)/5 = 1. The probability of a Z-score being less than 1 is 0.8413, so the probability of being no less than 55km is 1 - 0.8413 = 0.1587.

Question 10

Is between 2 and 4 minutes?

Accepted Answer

The answer of Is between 2 and 4 minutes?
...

Question 11

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 200?

Accepted Answer

In a normal distribution, the mean divides the distribution into two equal halves. Since 200 is the mean, 50% of the values lie above it and 50% below it. Therefore, the percentage of time the number of boxes received weekly will be greater than 200 is 50%.

Question 12

Suppose the distribution of integrity test scores is normally distributed with a mean of 15 and a variance of 25.Using this information,what percentage of the population scores between 10 and 20?

Accepted Answer

To find the percentage of the population that scores between 10 and 20, we use the properties of the normal distribution. The mean (μ) is 15, and the standard deviation (σ) is the square root of the variance, which is √25 = 5. We convert the scores 10 and 20 into z-scores: z = (X - μ) / σ. For X = 10, z = (10 - 15) / 5 = -1. For X = 20, z = (20 - 15) / 5 = 1. The percentage of the population between z = -1 and z = 1 in a standard normal distribution is approximately 68.26%.

Question 13

The distance between store outlets in a chain of stores in a large metropolitan city is normally distributed with an average of 50km and a standard deviation of 5km.What is the probability of finding a store between 50km and 60km?

Accepted Answer

The probability of finding a store between 50km and 60km is the area under the normal distribution curve between these two points. This is calculated using the Z-scores for 50km (Z=0) and 60km (Z=2). The cumulative probability for Z=2 is approximately 0.9772, and for Z=0 is 0.5. The difference is 0.4772.

Question 14

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 _____.

Accepted Answer

The correct answer is A because the z-score for a probability of 0.05 is -1.645. The z-score is calculated as (5.1 - x) / 0.5, where x is the average weight. Solving for x gives x = 4.278.

Question 15

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 85?

Accepted Answer

The answer of A company must decide their contribution to...

Question 16

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?

Accepted Answer

The answer of A company must decide their contribution to...

Question 17

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?

Accepted Answer

For a normal distribution, the median is equal to the mean. Therefore, 50% of the values are less than the mean, which is 200 in this case.

Question 18

When a ____________ probability distribution is used to approximate a ________ probability distribution we must make a ____________ correction.

Accepted Answer

A continuity correction is applied when a continuous probability distribution is used to approximate a discrete probability distribution, to adjust for the differences between the two types of distributions.

Question 19

Is no more than 3 minutes?

Accepted Answer

The answer of Is no more than 3 minutes?
...

Question 20

A probability distribution that is useful in describing the time or space between successive occurrences of an event is the _______ probability distribution.

Accepted Answer

The exponential probability distribution is commonly used to model the time or space between successive occurrences of an event. It has a continuous probability density function that is characterized by a single parameter, lambda (λ), which represents the mean number of occurrences in a given time interval or space. The exponential distribution is often used in queuing theory, reliability analysis, and other applications where the timing or distance between events is important.

Quiz 5: Continuous Random Variables

Exceeds 3 minutes?

A normal population has a mean of 10 and a variance of 4.What is P(X > 7) ?

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 less than 160?

Suppose the distribution of integrity test scores is normally distributed with a mean of 15 and a variance of 25.Using this information,what percentage of the population scores greater than 15?

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 between 180 and 210?

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?

A normal population has a mean of 10 and a variance of 4.What is P(X < 6) ?