Math  /  Data & Statistics

QuestionA recent survey showed that 93 full-time employees out of a sample of 400 did not use all of their vacation days last year. However, 118 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.
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Studdy Solution

STEP 1

1. The sample consists of 400 full-time employees.
2. 93 employees did not use all of their vacation days.
3. 118 employees expressed a desire for more vacation time.
4. An employee is content with their vacation allowance if they did not express a desire for more vacation time.

STEP 2

1. Determine the number of employees content with their vacation allowance.
2. Calculate the probability of selecting an employee who is content with their vacation allowance.

STEP 3

Calculate the number of employees content with their vacation allowance. This is the total number of employees minus those who expressed a desire for more vacation time.
400118=282 400 - 118 = 282

STEP 4

Calculate the probability that a randomly chosen employee is content with their vacation allowance. This is the number of content employees divided by the total number of employees.
Probability=282400 \text{Probability} = \frac{282}{400}

STEP 5

Simplify the fraction 282400\frac{282}{400} to its lowest terms.
Find the greatest common divisor (GCD) of 282 and 400, which is 2.
282÷2400÷2=141200 \frac{282 \div 2}{400 \div 2} = \frac{141}{200}
The probability that a randomly chosen employee is content with their vacation allowance is:
141200 \frac{141}{200}
or as a decimal:
0.705 0.705

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