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A survey of employed U.S. adults found that only 35% believe their employer cares about their well-being. You randomly select a sample of U.S. employees. Find the probability that fewer than 100 believe their employer cares about their well-being.

(Source: Gallup)

a. You select 250 U.S. employees.
b. You select 300 U.S. employees.
c. You select 400 U.S. employees.

Answer :

The probability that fewer than 100 U.S. employees believe their employer cares about their well-being is:

(a) approximately 0.0000.

(b) approximately 0.0000.

(c) approximately 0.0000.

To find the probability that fewer than 100 U.S. employees believe their employer cares about their well-being, we need to use the binomial distribution. The binomial distribution is appropriate here because we are dealing with a binary outcome (belief or non-belief) and randomly selecting a sample of employees.

The given survey states that only 35% of employed U.S. adults believe their employer cares about their well-being. This means the probability of an employee believing their employer cares is 0.35, and the probability of not believing is 0.65.

In scenario (a), where 250 U.S. employees are randomly selected, we calculate the probability of having fewer than 100 employees who believe their employer cares. Using the binomial probability formula, we sum the probabilities for 0, 1, 2, ..., 99 employees believing, which results in an extremely low probability of approximately 0.0000.

Similarly, in scenarios (b) and (c), where 300 and 400 U.S. employees are selected, respectively, the probability of fewer than 100 employees believing their employer cares is also approximately 0.0000.

These extremely low probabilities suggest that it is highly unlikely to randomly select such a small number of employees who believe their employer cares about their well-being, given the reported belief percentage in the survey.

Learn more about binomial distribution

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