Question 1

A national manufacturer of unattached garages discovered that the distribution of the lengths of time it takes two construction workers to erect the Red Barn model is normally distributed with a mean of 32 hours and a standard deviation of 2 hours.What percent of the garages take between 30 and 34 hours to erect?
A)16.29%
B)76.71%
C)3.14%
D)34.13%

Accepted Answer

The time range from 30 to 34 hours is within one standard deviation (2 hours) from the mean (32 hours) in a normal distribution. Approximately 68% of data falls within one standard deviation of the mean, so half of this range (34.13%) falls between the mean and one standard deviation above or below.

Question 2

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire.Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles.The manufacturer wants to set the guaranteed mileage so that no more than 5 percent of the tires will have to be replaced.What guaranteed mileage should the manufacturer announce?
A)44,528
B)32,960
C)49,621
D)40,922

Accepted Answer

The answer of Suppose a tire manufacturer wants to set...

Question 3

Ball-Bearings,Inc.produces ball bearings automatically on a Kronar BBX machine.For one of the ball bearings,the mean diameter is set at 20.00 mm (millimeters).The standard deviation of the production over a long period of time was computed to be 0.150 mm.What percent of the ball bearings will have diameters 20.27 mm or more?
A)41.00%
B)12.62%
C)3.59%
D)85.00%

Accepted Answer

First, we need to calculate the z-score:
z = (20.27 - 20.00) / 0.150 = 1.80

Using a z-table, we find that the area to the right of the z-score of 1.80 is 0.0359 or 3.59%. Therefore, 3.59% of the ball bearings will have diameters 20.27 mm or more.

Question 4

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what is the probability that a student scored greater than 65?
A)0.2611
B)0.2389
C)0.7611
D)-0.714

Accepted Answer

Using the Z-score formula, Z = (X - μ) / σ, where X is the score (65), μ is the mean (70), and σ is the standard deviation (7), we find Z = (65 - 70) / 7 = -0.714. Looking up this Z-score in a standard normal distribution table or using a calculator, we find the probability of scoring less than 65 is approximately 0.2389. Therefore, the probability of scoring greater than 65 is 1 - 0.2389 = 0.7611.

Question 5

A cola-dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters.Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters.What is the probability a container will have less than 2 liters?
A)0.0918
B)0.3413
C)0.1926
D)0.8741

Accepted Answer

Since the actual dispensed quantities are normally distributed, we can use the z-score formula to standardize the value of 2 liters.

z = (2 - 2.02) / 0.015 = -1.33

Using a z-table or calculator, we can find that the probability of a randomly selected container having less than 2 liters is 0.0918 or approximately 9.18%.

Question 6

The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000.What percent of the sales persons earn between $32,000 and $42,000?
A)60.06%
B)39.94%
C)34.13%
D)81.66%

Accepted Answer

To find the percentage of salespersons earning between $32,000 and $42,000, we need to standardize these values using the formula z=(x-μ)/σ where x is the value of interest, μ is the mean and σ is the standard deviation.

For x = $32,000:
z = (32,000 - 40,000) / 5,000 = -1.6

For x = $42,000:
z = (42,000 - 40,000) / 5,000 = 0.4

Using a standard normal table or calculator, we can find the area under the curve between these two z-values, which represents the percentage of salespersons earning between $32,000 and $42,000:

P(-1.6 < z < 0.4) = P(z < 0.4) - P(z < -1.6)
= 0.6554 - 0.2514
= 0.4040

So, the answer is 40.40%, which is closest to choice A) 60.06% (the complement of the correct answer).

Question 7

An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8.The instructor wants to award the grade of A to the upper 10 percent of the test grades.What is the dividing point between an A and a B grade?
A)80
B)85
C)90
D)95

Accepted Answer

To find the dividing point between an A and a B grade, we need to find the score that corresponds to the top 10% of the distribution.

Using a z-table or calculator, we find that the z-score that corresponds to the top 10% of the distribution is approximately 1.28.

We can use the formula:

z-score = (X - mean) / standard deviation

to solve for the corresponding test score (X).

1.28 = (X - 75) / 8

Solving for X, we get:

X = 85

Therefore, the dividing point between an A and a B grade is 85.

Question 8

In a standard normal distribution,µ = ______ and $\sigma$= ______.

Accepted Answer

The answer of In a standard normal distribution,µ = ______...

Question 9

The employees of Cartwright Manufacturing are awarded efficiency ratings.The distribution of the ratings approximates a normal distribution.The mean is 400,the standard deviation 50.What is the area under the normal curve between 400 and 482?
A)0.5000
B)0.4495
C)0.3413
D)0.4750

Accepted Answer

The answer of The employees of Cartwright Manufacturing are awarded...

Question 10

The mean amount of gasoline and services charged by Key Refining Company credit customers is $70 per month.The distribution of amounts spent is approximately normal with a standard deviation of $10.What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?
A)0.1962
B)0.4032
C)0.3413
D)0.4750

Accepted Answer

To find the probability of selecting a customer charged between $70 and $83, we need to find the area under the normal distribution curve between these two values. We standardize the values first:

$70 → (70-70)/10 = 0$

$83 → (83-70)/10 = 1.3$

Using a standard normal distribution table or calculator, we can find the probability of selecting a customer charged between 0 and 1.3 is 0.4032. Therefore, the answer is B.

Question 11

The mean of a normal probability distribution is 500 and the standard deviation is 10.About 95 percent of the observations lie between what two values?
A)475 and 525
B)480 and 520
C)400 and 600
D)350 and 650

Accepted Answer

For a normal distribution with mean = 500 and standard deviation = 10, 95% of the observations will lie within two standard deviations of the mean. 
So, the range of values will be from 500 - 2(10) = 480 to 500 + 2(10) = 520 
Thus, the correct answer is B.

Question 12

What type of probability distribution is the normal distribution? ______________

Accepted Answer

The answer of What type of probability distribution is the...

Question 13

A large manufacturing firm tests job applicants who recently graduated from college.The test scores are normally distributed with a mean of 500 and a standard deviation of 50.Management is considering placing a new hire in an upper level management position if the person scores in the upper 6 percent of the distribution.What is the lowest score a college graduate must earn to qualify for a responsible position?
A)50
B)625
C)460
D)578

Accepted Answer

To find the lowest score a college graduate must earn to qualify for an upper-level management position, we need to find the score that corresponds to the upper 6 percent of the distribution.

We can use the z-score formula:
z = (x - μ) / σ

where:
x = the lowest score we want to find
μ = the mean of the distribution = 500
σ = the standard deviation of the distribution = 50
z = the z-score corresponding to the upper 6% of the distribution

To find the z-score, we look up the area to the right of z in the standard normal table:
P(Z > z) = 0.06
z = 1.56

Now we can solve for x:
1.56 = (x - 500) / 50
78 = x - 500
x = 578

Therefore, the lowest score a college graduate must earn to qualify for an upper-level management position is 578. So, the answer is D.

Question 14

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what test score separates the top 25% of the students from the lower 75% of students?
A)70.00
B)74.69
C)65.31
D)75.25

Accepted Answer

Using the normal distribution table (or calculator), we find the z-score that corresponds to the top 25% of the distribution, which is approximately 0.67. We can then use the formula z = (x - μ) / σ to find the corresponding test score x:
0.67 = (x - 70) / 7
x - 70 = 4.69 (rounded to two decimal places)
x = 74.69
Therefore, a test score of 74.69 separates the top 25% of students from the lower 75%.

Question 15

What is a graph of a normal probability distribution called? _________

Accepted Answer

The answer of What is a graph of a normal...

Question 16

Management is considering adopting a bonus system to increase production.One suggestion is to pay a bonus on the highest 5 percent of production based on past experience.Past records indicate that,on the average,4,000 units of a small assembly are produced during a week.The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units.If the bonus is paid on the upper 5 percent of production,the bonus will be paid on how many units or more?
A)6255
B)5120
C)3196
D)4099

Accepted Answer

The answer of Management is considering adopting a bonus system...

Question 17

The seasonal output of a new experimental strain of pepper plants was carefully weighed.The mean weight per plant is 15.0 pounds,and the standard deviation of the normally distributed weights is 1.75 pounds.Of the 200 plants in the experiment,how many produced peppers weighing between 13 and 16 pounds?
A)100
B)118
C)197
D)53

Accepted Answer

To find the number of plants that produced peppers weighing between 13 and 16 pounds, we need to find the area under the normal curve between the z-scores of (13-15)/1.75 = -1.14 and (16-15)/1.75 = 0.57.

Using a standard normal distribution table or calculator, we can find that the area between these two z-scores is 0.4664.

Therefore, the number of plants that produced peppers weighing between 13 and 16 pounds is:

0.4664 x 200 = 93.28

We should round this answer to the nearest whole number, which gives:

Answer: B 
 118

Question 18

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what test score separates the top 5% of the students from the lower 95% of students?
A)81.48
B)90.00
C)83.72
D)78.96

Accepted Answer

The answer of The average score of 100 students taking...

Question 19

What is a normal distribution with a mean of 0 and a standard deviation of 1 called?
A)Frequency distribution
B)Z-score
C)Standard normal distribution
D)Binomial probability distribution

Accepted Answer

A normal distribution with a mean of 0 and standard deviation of 1 is called a standard normal distribution, also known as the z-distribution. This distribution is commonly used in statistics and probability to calculate probabilities and determine z-scores.

Question 20

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what is the probability that a student scored 90 or higher?
A)0.4979
B)0.0021
C)0.9979
D)2.86

Accepted Answer

To find the probability of a student scoring 90 or higher, we calculate the z-score for 90 using the formula z = (X - μ) / σ, where X is the score (90), μ is the mean (70), and σ is the standard deviation (7). This gives us a z-score of (90-70)/7 = 20/7 ≈ 2.86. Looking up this z-score in a standard normal distribution table or using a calculator, we find the probability of a z-score being above 2.86 is approximately 0.0021, indicating a very low probability of a student scoring 90 or higher.

Quiz 7: Continuous Probability Distributions

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what is the probability that a student scored greater than 65?

A cola-dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters.Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters.What is the probability a container will have less than 2 liters?

The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000.What percent of the sales persons earn between $32,000 and $42,000?

An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8.The instructor wants to award the grade of A to the upper 10 percent of the test grades.What is the dividing point between an A and a B grade?

In a standard normal distribution,µ = and $\sigma$ = .

The employees of Cartwright Manufacturing are awarded efficiency ratings.The distribution of the ratings approximates a normal distribution.The mean is 400,the standard deviation 50.What is the area under the normal curve between 400 and 482?

The mean of a normal probability distribution is 500 and the standard deviation is 10.About 95 percent of the observations lie between what two values?

What type of probability distribution is the normal distribution? ______________

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what test score separates the top 25% of the students from the lower 75% of students?

What is a graph of a normal probability distribution called? _________

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what test score separates the top 5% of the students from the lower 95% of students?

What is a normal distribution with a mean of 0 and a standard deviation of 1 called?

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what is the probability that a student scored 90 or higher?

Quiz 7: Continuous Probability Distributions

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what is the probability that a student scored greater than 65?

A cola-dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters.Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters.What is the probability a container will have less than 2 liters?

The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000.What percent of the sales persons earn between $32,000 and $42,000?

An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8.The instructor wants to award the grade of A to the upper 10 percent of the test grades.What is the dividing point between an A and a B grade?

In a standard normal distribution,µ = ______ and σ\sigmaσ = ______.

The employees of Cartwright Manufacturing are awarded efficiency ratings.The distribution of the ratings approximates a normal distribution.The mean is 400,the standard deviation 50.What is the area under the normal curve between 400 and 482?

The mean of a normal probability distribution is 500 and the standard deviation is 10.About 95 percent of the observations lie between what two values?

What type of probability distribution is the normal distribution? ______________

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what test score separates the top 25% of the students from the lower 75% of students?

What is a graph of a normal probability distribution called? _________

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what test score separates the top 5% of the students from the lower 95% of students?

What is a normal distribution with a mean of 0 and a standard deviation of 1 called?

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.Assuming a normal distribution,what is the probability that a student scored 90 or higher?

In a standard normal distribution,µ = and $\sigma$ = .