Question

the following data were gathered for 110 workers in two departments. of these workers, 49 were in department a, 6 workers in department a earned more than $80,000, and 34 workers in department b earned $80,000 or less. complete parts (a) through (d) below
(a) find the probability that a worker is in department a earning $80,000 or less
0.39
(type an integer or decimal rounded to two decimal places as needed.)
(b) find the probability that a worker is in department b earning more than $80,000
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Calculate number of workers in Department A earning $80,000 or less

Total workers in Department A is 49 and 6 workers in Department A earned more than $80,000. So number of workers in Department A earning $80,000 or less is $49 - 6=43$.

Step2: Calculate total number of workers

Total number of workers is 110.

Step3: Calculate probability for part (a)

Probability $P(A_{80 -})=\frac{43}{110}\approx 0.39$ (already given and verified).

Step4: Calculate number of workers in Department B

Number of workers in Department B is $110 - 49 = 61$.

Step5: Calculate number of workers in Department B earning more than $80,000

Number of workers in Department B earning $80,000 or less is 34. So number of workers in Department B earning more than $80,000 is $61 - 34 = 27$.

Step6: Calculate probability for part (b)

Probability $P(B_{>80})=\frac{27}{110}\approx 0.25$

Answer:

(a) 0.39
(b) 0.25