Question 1

The fares received by taxi drivers working for the City Taxi line are normally distributed with a mean of $12.50 and a standard deviation of $3.25.Based on this information,what is the probability that a specific fare will exceed $15.00?

Accepted Answer

The answer of The fares received by taxi drivers working...

Question 2

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,determine two values of which the smallest has 25% of the values below it and the largest has 25% of the values above it.
A)18.85 and 27.94
B)19.31 and 21.12
C)16.23 and 18.82
D)21.65 and 28.35

Accepted Answer

The values that have 25% of the observations below and above them are the first and third quartiles, respectively. In a normal distribution, these correspond to specific z-scores: approximately -0.675 for the first quartile and +0.675 for the third quartile. To find the actual values, use the formula: value = mean + (z-score * standard deviation). For the first quartile: 25 + (-0.675 * 5) = 21.625. For the third quartile: 25 + (0.675 * 5) = 28.375. These values are rounded to 21.65 and 28.35, respectively.

Question 3

For the normal distribution with parameters μ = 4,σ = 3;calculate P(x > 1).
A)0.8413
B)0.4562
C)0.7812
D)0.4152

Accepted Answer

To calculate P(x > 1) for a normal distribution with μ = 4 and σ = 3, we first find the z-score: z = (1 - 4) / 3 = -1. The table or calculator gives P(Z > -1) = 0.8413, since the normal distribution is symmetric and we're looking for the area to the right of z = -1.

Question 4

For the normal distribution with parameters μ = 5,σ = 4;calculate P(0 < x < 8).
A)0.8841
B)0.8812
C)0.4215
D)0.6678

Accepted Answer

The answer of For the normal distribution with parameters μ...

Question 5

In comparing a uniform distribution with a normal distribution where both distributions have the same mean and the same range,explain which distribution will have the larger standard deviation.

Accepted Answer

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Question 6

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will be exceeded 10% of the time?
A)31.40
B)28.60
C)66.23
D)14.56

Accepted Answer

To find the value exceeded 10% of the time, we need to find the 90th percentile of the normal distribution. Using the Z-table, the Z-score for 0.90 is approximately 1.28. Using the formula X = μ + Zσ, where μ = 25 and σ = 5, we get X = 25 + 1.28(5) = 31.40.

Question 7

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean.What is the probability that a randomly selected value from the distribution will be less than 2.1 standard deviations from the mean?
A)0.9488
B)0.9821
C)0.9976
D)0.9712

Accepted Answer

The answer of A randomly selected value from a normal...

Question 8

The fares received by taxi drivers working for the City Taxi line are normally distributed with a mean of $12.50 and a standard deviation of $3.25.Suppose a driver has four consecutive fares that are less than $6.00.What is the probability of this happening?

Accepted Answer

The answer of The fares received by taxi drivers working...

Question 9

If a continuous random variable is said to be exponentially distributed,what would be the easiest way to reduce the standard deviation?

Accepted Answer

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Question 10

The money spent by people at an amusement park,after paying to get in the gate,is thought to be uniformly distributed between $5.00 and $25.00.Based on this,what is the probability that someone will spend between $8.00 and $12.00?

Accepted Answer

The answer of The money spent by people at an...

Question 11

What is the difference between a normal distribution and the standard normal distribution?

Accepted Answer

The answer of What is the difference between a normal...

Question 12

For the normal distribution with parameters μ = 0,σ = 3;calculate P(x > 1).
A)0.5812
B)0.1214
C)0.3707
D)0.4412

Accepted Answer

We need to standardize the given value first:
z = (1 - μ) / σ = (1 - 0) / 3 = 0.3333
Now, we can find the probability using a standard normal distribution table or calculator:
P(x > 1) = P(z > 0.3333) = 1 - P(z < 0.3333) = 1 - 0.6293 = 0.3707
Therefore, the best choice is (C).

Question 13

For the normal distribution with parameters μ = 5,σ= 2;calculate P(0 < x < 8).
A)0.8023
B)0.4152
C)0.9270
D)0.8845

Accepted Answer

We need to standardize the values of x using the formula z = (x-μ)/σ.

So, for x=0, z = (0-5)/2 = -2.5 and for x=8, z = (8-5)/2 = 1.5.

Using a standard normal distribution table, the probability of z being between -2.5 and 1.5 is 0.9270. Therefore, the answer is C.

Question 14

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will 15% of the observations be below?
A)19.8
B)16.2
C)18.7
D)17.2

Accepted Answer

The answer of A random variable is normally distributed with...

Question 15

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean.What is the probability that a randomly selected value from the distribution will be greater than 2.1 standard deviations above the mean?
A)0.0179
B)0.0512
C)0.0231
D)0.0024

Accepted Answer

From the standard normal distribution table, the area to the right of 2.1 standard deviations is 0.0179, which represents the probability of selecting a value greater than 2.1 standard deviations above the mean.

Question 16

For the normal distribution with parameters μ = 3,σ = 2;calculate P(0 < x < 8).
A)0.3124
B)0.9270
C)0.8123
D)0.6723

Accepted Answer

We need to find the area under the normal curve between x=0 and x=8. 
Using standardization, z=(x-μ)/σ=(0-3)/2=-1.5 and z=(8-3)/2=2.5 
Now, we look up the area between -1.5 and 2.5 in the standard normal distribution table or calculator, which is approximately 0.9270. Therefore, the answer is B.

Question 17

A class takes an exam where the average time to complete the exam is normally distributed with a time of 40 minutes and standard deviation of 9 minutes.If the class lasts 1 hour,what percent of the students will have turned in the exam after 60 minutes?

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Question 18

The weight of sacks of potatoes is normally distributed with a mean of 20 pounds and a standard deviation of 2 pounds.The weight of sacks of onions is also normally distributed with a mean of 20 pounds and a standard deviation of 0.50 pounds.Based on this information,which product will yield the highest probability of getting a very heavy sack?

Accepted Answer

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Question 19

A random variable,x,has a normal distribution with μ = 13.6 and σ = 2.90.Determine a value,x₀,so that P(μ - x₀ ≤ x ≤ μ + x₀)= 0.95. A)7.916 B)4.535 C)3.178 D)9.425

Accepted Answer

The correct answer is A because the value of x0 that satisfies the given probability is 7.916. This can be calculated using the standard normal distribution (z-distribution) and the formula: P(μ - x0 ≤ x ≤ μ + x0) = 0.95 = P(-z0 ≤ z ≤ z0) = 2Φ(z0) - 1, where Φ(z) is the cumulative distribution function of the standard normal distribution. Solving for z0 gives z0 = 1.96. Then, using the formula z0 = (x0 - μ) / σ, we get x0 = μ + z0 * σ = 13.6 + 1.96 * 2.90 = 7.916.

Question 20

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will be exceeded 85% of the time?
A)16.2
B)17.9
C)19.8
D)14.2

Accepted Answer

The answer of A random variable is normally distributed with...

Quiz 6: Introduction to Continuous Probability Distributions

The fares received by taxi drivers working for the City Taxi line are normally distributed with a mean of $12.50 and a standard deviation of $3.25.Based on this information,what is the probability that a specific fare will exceed $15.00?

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,determine two values of which the smallest has 25% of the values below it and the largest has 25% of the values above it.

For the normal distribution with parameters μ = 4,σ = 3;calculate P(x > 1) .

For the normal distribution with parameters μ = 5,σ = 4;calculate P(0 < x < 8) .

In comparing a uniform distribution with a normal distribution where both distributions have the same mean and the same range,explain which distribution will have the larger standard deviation.

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will be exceeded 10% of the time?

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean.What is the probability that a randomly selected value from the distribution will be less than 2.1 standard deviations from the mean?

The fares received by taxi drivers working for the City Taxi line are normally distributed with a mean of $12.50 and a standard deviation of $3.25.Suppose a driver has four consecutive fares that are less than $6.00.What is the probability of this happening?

If a continuous random variable is said to be exponentially distributed,what would be the easiest way to reduce the standard deviation?

The money spent by people at an amusement park,after paying to get in the gate,is thought to be uniformly distributed between $5.00 and $25.00.Based on this,what is the probability that someone will spend between $8.00 and $12.00?

What is the difference between a normal distribution and the standard normal distribution?

For the normal distribution with parameters μ = 0,σ = 3;calculate P(x > 1) .

For the normal distribution with parameters μ = 5,σ= 2;calculate P(0 < x < 8) .

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will 15% of the observations be below?

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean.What is the probability that a randomly selected value from the distribution will be greater than 2.1 standard deviations above the mean?

For the normal distribution with parameters μ = 3,σ = 2;calculate P(0 < x < 8) .

A class takes an exam where the average time to complete the exam is normally distributed with a time of 40 minutes and standard deviation of 9 minutes.If the class lasts 1 hour,what percent of the students will have turned in the exam after 60 minutes?

A random variable,x,has a normal distribution with μ = 13.6 and σ = 2.90.Determine a value,x₀,so that P(μ - x₀ ≤ x ≤ μ + x₀) = 0.95.

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will be exceeded 85% of the time?

Quiz 6: Introduction to Continuous Probability Distributions

The fares received by taxi drivers working for the City Taxi line are normally distributed with a mean of $12.50 and a standard deviation of $3.25.Based on this information,what is the probability that a specific fare will exceed $15.00?

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,determine two values of which the smallest has 25% of the values below it and the largest has 25% of the values above it.

For the normal distribution with parameters μ = 4,σ = 3;calculate P(x > 1) .

For the normal distribution with parameters μ = 5,σ = 4;calculate P(0 < x < 8) .

In comparing a uniform distribution with a normal distribution where both distributions have the same mean and the same range,explain which distribution will have the larger standard deviation.

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will be exceeded 10% of the time?

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean.What is the probability that a randomly selected value from the distribution will be less than 2.1 standard deviations from the mean?

The fares received by taxi drivers working for the City Taxi line are normally distributed with a mean of $12.50 and a standard deviation of $3.25.Suppose a driver has four consecutive fares that are less than $6.00.What is the probability of this happening?

If a continuous random variable is said to be exponentially distributed,what would be the easiest way to reduce the standard deviation?

The money spent by people at an amusement park,after paying to get in the gate,is thought to be uniformly distributed between $5.00 and $25.00.Based on this,what is the probability that someone will spend between $8.00 and $12.00?

What is the difference between a normal distribution and the standard normal distribution?

For the normal distribution with parameters μ = 0,σ = 3;calculate P(x > 1) .

For the normal distribution with parameters μ = 5,σ= 2;calculate P(0 < x < 8) .

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will 15% of the observations be below?

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean.What is the probability that a randomly selected value from the distribution will be greater than 2.1 standard deviations above the mean?

For the normal distribution with parameters μ = 3,σ = 2;calculate P(0 < x < 8) .

A class takes an exam where the average time to complete the exam is normally distributed with a time of 40 minutes and standard deviation of 9 minutes.If the class lasts 1 hour,what percent of the students will have turned in the exam after 60 minutes?

A random variable,x,has a normal distribution with μ = 13.6 and σ = 2.90.Determine a value,x0,so that P(μ - x0 ≤ x ≤ μ + x0) = 0.95.

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will be exceeded 85% of the time?

A random variable,x,has a normal distribution with μ = 13.6 and σ = 2.90.Determine a value,x₀,so that P(μ - x₀ ≤ x ≤ μ + x₀) = 0.95.