Given that from an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. Here, p denotes the probability of success and q denotes the probability of failure such that p + q = 1. For the given problem p=12/48=1/4, and q=1−p=3/4. Therefore,
1. The probability out of the 8 new cars it just received that when each is tested, no more than 2 of the cars have defective radios is as follows:This is a binomial probability question where n = 8, x = 0, 1 or 2.So, P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)This is calculated as follows: P(X=0) = C(8, 0) (1/4)^0 (3/4)^8 = 0.1001P(X=1) = C(8, 1) (1/4)^1 (3/4)^7 = 0.3004P(X=2) = C(8, 2) (1/4)^2 (3/4)^6 = 0.3299Therefore, P(X ≤ 2) = 0.1001 + 0.3004 + 0.3299 = 0.7304Thus, the probability is 0.7304.
2. The probability out of the 8 new cars it just received that when each is tested, exactly half of the cars have defective radios is as follows:This is a binomial probability question where n = 8, x = 4.So, P(X = 4) = C(8, 4) (1/4)^4 (3/4)^4 = 0.0865Thus, the probability is 0.0865.3.
3. The probability out of the 8 new cars it just received that when each is tested, none of the cars have defective radios is as follows:This is a binomial probability question where n = 8, x = 0.So, P(X = 0) = C(8, 0) (1/4)^0 (3/4)^8 = 0.1001Thus, the probability is 0.1001.4.
4. The probability out of the 8 new cars it just received that when each is tested, no more than 2 of the cars have defective radios is as follows:This is a binomial probability question where n = 8, x = 0, 1 or 2.So, P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)This is calculated as follows: P(X=0) = C(8, 0) (1/4)^0 (3/4)^8 = 0.1001P(X=1) = C(8, 1) (1/4)^1 (3/4)^7 = 0.3004P(X=2) = C(8, 2) (1/4)^2 (3/4)^6 = 0.3299Therefore, P(X ≤ 2) = 0.1001 + 0.3004 + 0.3299 = 0.7304Thus, the probability is 0.7304.
5. The probability out of the 8 new cars it just received that when each is tested, no more than half of the cars have non-defective radios is as follows:This is a binomial probability question where n = 8, x = 0, 1, 2, 3, or 4.So, P(X ≤ 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)This is calculated as follows: P(X=0) = C(8, 0) (1/4)^0 (3/4)^8 = 0.1001P(X=1) = C(8, 1) (1/4)^1 (3/4)^7 = 0.3004P(X=2) = C(8, 2) (1/4)^2 (3/4)^6 = 0.3299P(X=3) = C(8, 3) (1/4)^3 (3/4)^5 = 0.1852P(X=4) = C(8, 4) (1/4)^4 (3/4)^4 = 0.0477Therefore, P(X ≤ 4) = 0.1001 + 0.3004 + 0.3299 + 0.1852 + 0.0477 = 1.0633Thus, the probability is 1.0633.
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The rate of return of a Fortune 500 company over the past 15 years are: 3.17%, 4.43%, 5.93%, 5.43%, 7.29%, 8.21%, 6.23%, 5.23%,
4.34%, 6.68%, 7.14%, -5.56%, -5.23%, -5.73%, -10.34%
1. Compute the arithmetic mean rate of return per year.
2. Compute the geometric mean rate of return per year for the first four years.
3. Construct a boxplot for the rate of return. What is the shape of the distribution for the rate of return?
1. The arithmetic mean rate of return per year is approximately 3.96%. 2. The geometric mean rate of return per year for the first four years is approximately 1.06%. 3. The shape of the distribution for the rate of return is negatively skewed.
1. To compute the arithmetic mean rate of return per year, we sum up the rates of return for the 15 years and divide by the number of years.
Arithmetic mean = (3.17% + 4.43% + 5.93% + 5.43% + 7.29% + 8.21% + 6.23% + 5.23% + 4.34% + 6.68% + 7.14% - 5.56% - 5.23% - 5.73% - 10.34%) / 15
= 59.45% / 15
= 3.9633%
Therefore, the arithmetic mean rate of return per year is approximately 3.96%.
2. To compute the geometric mean rate of return per year for the first four years, we multiply the individual rates of return and then take the fourth root.
Geometric mean = (1 + 0.0317) × (1 + 0.0443) × (1 + 0.0593) × (1 + 0.0543)^(1/4)
= (1.0317 × 1.0443 × 1.0593 × 1.0543)^(1/4)
= 1.0425^(1/4)
= 1.0106 - 1
= 1.06%
Therefore, the geometric mean rate of return per year for the first four years is approximately 1.06%.
3. To construct a boxplot for the rate of return, we need to determine the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
The boxplot provides a visual representation of the distribution and identifies outliers.
The five-number summary is as follows:
Minimum: -10.34%
Q1: -5.73%
Median: 4.34%
Q3: 6.23%
Maximum: 8.21%
The boxplot will show a box with the median (Q2) as a line inside it, with the lower end of the box at Q1 and the upper end at Q3. The whiskers extend from the box to the minimum and maximum values, respectively. Any data points beyond the whiskers are considered outliers.
Based on the given data, the shape of the distribution for the rate of return is negatively skewed. This is evident from the fact that the mean is lower than the median, and the presence of negative returns pulls the overall distribution towards the left.
The outliers, represented by the minimum and maximum values, also contribute to the asymmetry of the distribution.
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Given below is the stem-and-leaf display representing the amount of detergent used in gallons (with leaves in 10ths of gallons) in a day by 25 drive-through car wash operations in Phoenix.
9 | 147
10 | 02238
11 | 135566777
12 | 223489
13 | 02
1. Suppose that a percentage histogram for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class. Determine the percentage of drive-through car wash operations that use “12.0 but less than 13.0 gallons” of detergent?
2. If a percentage histogram for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drive-through car wash operations use less than 12 gallons of detergent in a day?
3. If a relative frequency or percentage distribution for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drive-through car wash operations use at least 10 gallons of detergent in a day?
4. Construct a relative frequency or percentage distribution for the detergent data, using "9.0 but less than 10.0" as the first class.
5. Construct a cumulative percentage distribution for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class.
6. Construct a percentage histogram for the detergent data, using "9.0 but less than 10.0" as the first class.
7. Construct a cumulative percentage polygon for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class.
8. Construct a percentage polygon for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class.
96% of the drive-through car wash operations use at least 10 gallons of detergent in a month.
To construct a relative frequency or percentage distribution, we first need to organize the given data into a frequency table. Let's do that:
Class Interval Frequency
---------------------------------
9.0 - 10.0 1
10.0 - 11.0 8
11.0 - 12.0 5
12.0 - 13.0 6
13.0 - 14.0 5
Now, let's calculate the total number of drive-through car wash operations, which is the sum of all frequencies: 1 + 8 + 5 + 6 + 5 = 25.
To determine the percentage of drive-through car wash operations that use at least 10 gallons of detergent in a month, we need to consider the classes from 10.0 gallons onwards.
These are the classes 10.0 - 11.0, 11.0 - 12.0, 12.0 - 13.0, and 13.0 - 14.0. The frequencies for these classes are 8, 5, 6, and 5, respectively.
The total frequency for classes with at least 10 gallons is 8 + 5 + 6 + 5 = 24. To calculate the percentage, divide this frequency by the total number of drive-through car wash operations (25) and multiply by 100:
Percentage = (24/25) * 100 = 96%
Therefore, approximately 96% of the drive-through car wash operations use at least 10 gallons of detergent in a month.
Please note that the provided stem-and-leaf display appears to have some irregularities, such as multiple leaves for some stems. It's important to verify the accuracy of the given data to ensure precise calculations.
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The probable question may be:
Given below is the stem-and-leaf display representing the amount of detergent used in gallons (with leaves in 10 ths of gallons) in a month by 25 drive-through car wash operations in Phoenix.
steams:- 9,10,11,12,13
Leaves:- 147,02238,135566777,223489,02
If a relative frequency or percentage distribution for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drive-through car wash operations use at least 10 gallons of detergent in a month?
A system of organizations, people, activities, information, and resources involved in supplying a product or service to a consumer is called the
A system of organizations, people, activities, information, and resources involved in supplying a product or service to a consumer is called a supply chain.
A supply chain encompasses the entire process of delivering a product or service to a consumer, involving various interconnected components. Let's break down the elements of a supply chain:
Organizations: It involves multiple organizations, such as suppliers, manufacturers, distributors, wholesalers, retailers, and even service providers. These entities collaborate and interact to ensure the smooth flow of products or services.People: Individuals within each organization play crucial roles in the supply chain. They include managers, employees, logistics personnel, sales representatives, and other stakeholders involved in various activities throughout the chain.Activities: The supply chain encompasses a range of activities, including procurement, production, inventory management, transportation, warehousing, order fulfillment, and customer service. Each activity contributes to the overall process of delivering the product or service to the consumer.Information: Information flows throughout the supply chain, enabling coordination, decision-making, and synchronization. It includes data on inventory levels, customer orders, production schedules, logistics tracking, and demand forecasts.Resources: Various resources are required in a supply chain, such as raw materials, equipment, facilities, transportation vehicles, and financial capital. Effective resource management is crucial for optimizing the supply chain's performance.In summary, a supply chain integrates organizations, people, activities, information, and resources to ensure the efficient and effective delivery of products or services from suppliers to consumers.
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