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According to Mediamark Research, 84 million out of 179 million adults in the United States correct their vision by using prescription eyeglasses, bifocals, or contact lenses. (Some respondents use more than one type.) What is the probability that an adult selected at random from the adult population uses corrective lenses?

Short Answer

Expert verified
The probability that a randomly selected adult from the adult population in the United States uses corrective lenses is approximately 0.46927 or 46.93%.

Step by step solution

01

Identify the given information

We are given the following information: - Total number of adults in the United States: 179 million - Number of adults using corrective lenses: 84 million
02

Calculate the probability

To find the probability that a randomly selected adult uses corrective lenses, we can use the formula: probability = \(\frac{\text{number of desired outcomes}}{\text{total number of possible outcomes}}\) In this case, the number of desired outcomes is the number of adults using corrective lenses (84 million), and the total number of possible outcomes is the total number of adults in the United States (179 million). probability = \(\frac{84 \,\text{million}}{179 \,\text{million}}\)
03

Simplify the expression

Now, we can simplify the expression and get the probability in decimal form. probability = \( \frac{84}{179}\) probability ≈ 0.46927 The probability that a randomly selected adult from the adult population in the United States uses corrective lenses is approximately 0.46927 or 46.93%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Corrective Lenses Statistics
When discussing statistics related to corrective lenses in the United States, it's essential to understand the context and significance of these numbers. Corrective lenses include eyeglasses, bifocals, or contact lenses. It reflects a common need among the population to enhance vision clarity.

For instance, according to a study, out of 179 million adults in the U.S., 84 million are reported to use some form of corrective lenses. This amounts to a substantial portion of the population, indicating a widespread reliance on optical correction for basic visual functions.

These types of statistics are crucial for various stakeholders, including healthcare providers, policymakers, and the lens-manufacturing industry. Understanding these numbers helps in resource allocation and planning for public health strategies.
Mathematical Reasoning
In solving probability-related problems, a clear grasp of mathematical reasoning is vital. This exercise involves reasoning through the relationships between given values to determine a probability.

The first step in the process involved identifying the total number of adults and those using corrective lenses. This involves a clear description of a part (corrective lenses users) compared to a whole (total adult population).

Once identified, you are tasked with organizing this information in a manner that can be manipulated mathematically – here, using the probability formula. This formula, comparing the number of favorable outcomes to the total possible outcomes, is a foundational concept in probability politics. - Recognize relevant data: Start by identifying essential numbers and what they represent. - Establish relationships: See how these numbers interact to express broader realities in probability. - Apply mathematical concepts: Use established formulas to derive meaningful statistics.
Probability Calculation
Probability calculation is a fundamental aspect of statistics and is key in predicting outcomes in uncertain situations. To compute probability, one needs a clear understanding of the formula used: \[\text{Probability} = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \]

In our example, the 'favorable outcome' is an adult using corrective lenses, which is 84 million. The 'total possible outcomes' represents the entire adult population, which is 179 million.

By placing the values into our formula, we find:\[\text{Probability} = \frac{84}{179} \]This results in approximately 0.46927, meaning there's a 46.93% chance a randomly chosen adult uses corrective lenses. Such computations help us understand events' likelihood in statistical terms, critical for effective decision-making.

In sum, probability calculation is a powerful tool to anticipate and understand data trends and behaviors within a population. Understanding this helps in numerous fields, including health, marketing, and engineering.

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Most popular questions from this chapter

In a Los Angeles Times poll of 1936 California residents conducted in February 2004 , the following question was asked: Do you favor or oppose an amendment to the U.S. Constitution barring same-sex marriage? The following results were obtained: $$ \begin{array}{lccc} \hline \text { Opinion } & \text { Favor } & \text { Oppose } & \text { Don't know } \\ \hline \text { Respondents } & 910 & 891 & 135 \\ \hline \end{array} $$ Determine the empirical probability distribution associated with these data.

In an online survey of 500 adults living with children under the age of \(18 \mathrm{yr}\), the participants were asked how many days per week they cook at home. The results of the survey are summarized below: $$ \begin{array}{lcccccccc} \hline \text { Number of Days } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text { Respondents } & 25 & 30 & 45 & 75 & 55 & 100 & 85 & 85 \\ \hline \end{array} $$ Determine the empirical probability distribution associated with these data.

In a survey of 200 employees of a company regarding their \(401(\mathrm{k})\) investments, the following data were obtained: 141 had investments in stock funds. 91 had investments in bond funds. 60 had investments in money market funds. 47 had investments in stock funds and bond funds. 36 had investments in stock funds and money market funds. 36 had investments in bond funds and money market funds. 22 had investments in stock funds, bond funds, and money market funds. What is the probability that an employee of the company chosen at random a. Had investments in exactly two kinds of investment funds? b. Had investments in exactly one kind of investment fund? c. Had no investment in any of the three types of funds?

A time study was conducted by the production manager of Vista Vision to determine the length of time in minutes required by an assembly worker to complete a certain task during the assembly of its Pulsar color television sets. a. Describe a sample space corresponding to this time study. b. Describe the event \(E\) that an assembly worker took 2 min or less to complete the task. c. Describe the event \(F\) that an assembly worker took more than 2 min to complete the task.

In an attempt to study the leading causes of airline crashes, the following data were compiled from records of airline crashes from 1959 to 1994 (excluding sabotage and military action). $$ \begin{array}{lc} \hline \text { Primary Factor } & \text { Accidents } \\ \hline \text { Pilot } & 327 \\ \hline \text { Airplane } & 49 \\ \hline \text { Maintenance } & 14 \\ \hline \text { Weather } & 22 \\ \hline \text { Airport/air traffic control } & 19 \\ \hline \text { Miscellaneous/other } & 15 \\ \hline \end{array} $$ Assume that you have just learned of an airline crash and that the data give a generally good indication of the causes of airline crashes. Give an estimate of the probability that the primary cause of the crash was due to pilot error or bad weather.

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