Question 1

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The probability that X will take on a value of at least 26 is
A) 0.000
B) 0.125
C) 0.250
D) 1.000

Accepted Answer

Since X has a uniform distribution over the interval from 20 to 28, the probability density function is constant over this interval, and equals 1/(28-20) = 1/8. The probability that X will take on a value of at least 26 is the area under the probability density function from 26 to 28, which is (1/8)*(28-26) = 1/4 = 0.250. Therefore, the correct choice is C.

Question 2

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The expected assembly time in minutes) is
A) 16
B) 2
C) 8
D) 4

Accepted Answer

The expected value of a uniformly distributed variable is the average of the minimum and maximum values, which in this case is (6+10)/2 = 8.

Question 3

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The probability of assembling the product in less than 6 minutes is
A) zero
B) 0.50
C) 0.15
D) 1

Accepted Answer

If the assembly time is uniformly distributed between 6 to 10 minutes, that means it is impossible to assemble the product in less than 6 minutes. Therefore, the probability of assembling the product in less than 6 minutes is zero.

Question 4

Z is a standard normal random variable. The P-1.5 ≤ Z ≤ 1.09) equals
A) 0.4322
B) 0.3621
C) 0.7953
D) 0.0711

Accepted Answer

Using a standard normal table or calculator, we find that P(Z ≤ 1.09) = 0.8621 and P(Z ≤ -1.5) = 0.0668. Therefore, P(-1.5 ≤ Z ≤ 1.09) = 0.8621 - 0.0668 = 0.7953.

Question 5

Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901?
A) 1.96
B) -1.96
C) 0.4505
D) ±1.65

Accepted Answer

The answer of Given that Z is a standard normal...

Question 6

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The probability density function has what value in the interval between 20 and 28?
A) 0
B) 0.050
C) 0.125
D) 1.000

Accepted Answer

The answer of Exhibit 6-3
Consider the continuous random variable X,...

Question 7

Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?
A) 1.8
B) 1.54
C) 2.1
D) 1.77

Accepted Answer

The answer of Given that Z is a standard normal...

Question 8

In a standard normal distribution the value of z
A) can be any value
B) cannot be negative
C) cannot be larger than 3.09
D) cannot be larger than 0.50

Accepted Answer

The answer of In a standard normal distribution the value...

Question 9

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.9834?
A) 0.4834
B) -2.13
C) +2.13
D) zero

Accepted Answer

The answer of Given that Z is a standard normal...

Question 10

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The probability of assembling the product in 7 minutes or more is
A) 0.25
B) 0.75
C) zero
D) 1

Accepted Answer

The probability of assembling the product in 7 minutes or more can be calculated by finding the area of the uniform distribution from 7 to 10 minutes. This area is (10-7)/(10-6) = 3/4 = 0.75, which is the probability of assembling the product in 7 minutes or more. Therefore, the correct choice is B.

Question 11

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The probability density function has what value in the interval between 6 and 10?
A) 0.25
B) 4.00
C) 5.00
D) zero

Accepted Answer

The probability density function for a uniform distribution is constant, so the value is simply 1/(10-6) = 0.25 in the interval from 6 to 10. Therefore, the correct choice is A.

Question 12

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The probability of assembling the product between 7 to 9 minutes is
A) zero
B) 0.50
C) 0.20
D) 1

Accepted Answer

The answer of Exhibit 6-1
The assembly time for a product...

Question 13

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The probability that X will take on a value between 21 and 25 is
A) 0.125
B) 0.250
C) 0.500
D) 1.000

Accepted Answer

The answer of Exhibit 6-3
Consider the continuous random variable X,...

Question 14

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-2. What is the minimum weight of the middle 95% of the players?
A) 196
B) 151
C) 249
D) 190

Accepted Answer

The answer of Exhibit 6-2
The weight of football players is...

Question 15

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?
A) 1.08
B) 0.1401
C) 2.16
D) -1.08

Accepted Answer

The answer of Given that Z is a standard normal...

Question 16

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds?
A) 28.81%
B) 0.5762%
C) 0.281%
D) 57.62%

Accepted Answer

The answer of Exhibit 6-2
The weight of football players is...

Question 17

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.119?
A) 0.381
B) +1.18
C) -1.18
D) 2.36

Accepted Answer

Using a standard normal table, we can find that the closest area to 0.119 in the table is 0.1179, which corresponds to a Z-value of -1.18. Therefore, Choice C is the correct answer.

Question 18

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-2. The probability of a player weighing more than 241.25 pounds is
A) 0.4505
B) 0.0495
C) 0.9505
D) 0.9010

Accepted Answer

We need to find the z-score for a weight of 241.25.

z = (241.25-200)/25 = 1.65

Using a standard normal table, we find the probability of a z-score larger than 1.65 to be 0.0495. Therefore, the answer is B.

Question 19

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The standard deviation of assembly time in minutes) is approximately
A) 1.3333
B) 1.1547
C) 0.1111
D) 0.5773

Accepted Answer

The formula for the standard deviation of a uniform distribution is (b-a)/sqrt(12), where a is the minimum value and b is the maximum value. 
In this case, a=6 and b=10. 
Plugging in the values, we get: 
SD = (10-6)/sqrt(12) 
SD = 4/sqrt(12) 
SD = 1.1547 (rounded to four decimal places) 
Therefore, the best choice for the standard deviation is B) 1.1547.

Question 20

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-2. The probability of a player weighing less than 250 pounds is
A) 0.4772
B) 0.9772
C) 0.0528
D) 0.5000

Accepted Answer

To solve this problem, we need to use the standard normal distribution. We can convert the weight of 250 pounds to a standardized value using the formula:

z = (x - μ) / σ

where z is the standardized value, x is the weight we want to find the probability for, μ is the mean, and σ is the standard deviation.

Plugging in the values given, we get:

z = (250 - 200) / 25 = 2

Next, we need to find the probability of a player weighing less than 250 pounds, which is equivalent to finding the area under the standard normal distribution curve to the left of z = 2. We can look up this probability in a standard normal distribution table or use a calculator to find that:

P(z < 2) = 0.9772

Therefore, the answer is B.

Quiz 6: Continuous Probability Distributions

Exhibit 6-3 Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-3. The probability that X will take on a value of at least 26 is

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The expected assembly time in minutes) is

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The probability of assembling the product in less than 6 minutes is

Z is a standard normal random variable. The P-1.5 ≤ Z ≤ 1.09) equals

Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901?

Exhibit 6-3 Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-3. The probability density function has what value in the interval between 20 and 28?

Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?

In a standard normal distribution the value of z

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.9834?

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The probability of assembling the product in 7 minutes or more is

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The probability density function has what value in the interval between 6 and 10?

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The probability of assembling the product between 7 to 9 minutes is

Exhibit 6-3 Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-3. The probability that X will take on a value between 21 and 25 is

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-2. What is the minimum weight of the middle 95% of the players?

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds?

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.119?

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-2. The probability of a player weighing more than 241.25 pounds is

Exhibit 6-1 The assembly time for a product is uniformly distributed between 6 to 10 minutes. -Refer to Exhibit 6-1. The standard deviation of assembly time in minutes) is approximately

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-2. The probability of a player weighing less than 250 pounds is