A sample of 500 full-time employees were surveyed on their feelings about their benefits package. 78 of those studied did not use all of their vacation days last year, yet 94 of those studied expressed a desire for more vacation time. Based on this sample, if a full-time employee is chosen at random, what is the probability that he or she is content with the vacation allowance? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
To find the probability that a full-time employee is content with the vacation allowance, we need to find the ratio of the number of employees who are content with the vacation allowance to the total number of employees in the sample.
Out of the 500 employees surveyed, 78 did not use all of their vacation days and expressed a desire for more vacation time. This means that 500 - 78 = <<500-78=422>>422 employees did not express a desire for more vacation time.
Therefore, the probability that an employee is content with the vacation allowance is 422/500 = 0.844.
Rounded to the nearest millionth, the probability is 0.844.
To find the probability that a randomly chosen full-time employee is content with the vacation allowance, we need to determine the number of employees surveyed who used all of their vacation days last year and expressed a desire for more vacation time.
From the information given:
- 78 employees did not use all of their vacation days last year
- 94 employees expressed a desire for more vacation time
To find the number of employees who used all of their vacation days last year:
Total number of employees surveyed - Number of employees who did not use all of their vacation days last year
= 500 - 78
= 422
Therefore, the number of employees who used all of their vacation days last year and expressed a desire for more vacation time is 422.
The probability that a full-time employee is content with the vacation allowance is given by:
Number of employees who used all of their vacation days last year and expressed a desire for more vacation time / Total number of employees surveyed
= 422 / 500
= 0.844
Expressed as a fraction in lowest terms, the probability is 422/500, which can be simplified further if needed.
To find the probability that a randomly chosen full-time employee is content with the vacation allowance based on the given sample, we need to determine the number of employees who are content with the vacation allowance and divide it by the total number of employees in the sample.
From the given information, we can conclude that:
- Out of the 500 employees surveyed, 78 did not use all of their vacation days last year. This means that these 78 employees are content with the vacation allowance.
- Additionally, 94 employees expressed a desire for more vacation time. However, it is not explicitly stated whether these 94 employees used all of their vacation days or not. Therefore, we cannot make a direct assumption about their contentment with the vacation allowance.
Since we are only considering the employees who did not use all of their vacation days (78 out of 500), we can calculate the probability as follows:
Probability (content with vacation allowance) = Number of employees content / Total number of employees
Probability (content with vacation allowance) = 78 / 500
Now, we can simplify this fraction to its lowest terms:
Probability (content with vacation allowance) = 3 /20
Therefore, the probability that a randomly chosen full-time employee is content with the vacation allowance is 3/20 or 0.15 (rounded to the nearest hundredth).