Math  /  Data & Statistics

QuestionFactory workers are constantly encouraged to practice zero tolerance when it comes to accidents in factories. Accidents can occur because the working environment or conditions themselves are unsafe On the other hand, accidents can occur due to carelessness or so-called human error. In addition, the worker's shift, 7:00 A.M. to 3:00 P.M. (day shift), 3:00 P.M. to 11:0011: 00 P.M. (evening shift), or 11.00 P.M. to 7.00 A.M. (graveyard shift), may be a factor. During the last year, 300 accidents have occurred. The percentages of the accidents for the condition combinations are shown in the accompanying table. Complete parts (a) through (d) below.
Click the icon to view the data on accidents. (a) If an accident report is selected randomly from the 300 reports, what is the probability that the accident occurred on the evening shift? (Type an integer or a decimal. Do not round.) (b) If an accident report is selected randomly from the 300 reports, what is the probability that the accident occurred due to human error? (Type an integer or a decimal. Do not round.) (c) If an accident report is selected randomly from the 300 reports, what is the probability that the accident occurred due to unsafe conditions? (Type an integer or a decimal. Do not round.) (d) If an accident report is selected randomly from the 300 reports, what is the probability that the accident occurred on either the evening or the graveyard shift? \square (Type an integer or a decimal. Do not round.) Factory Accidents \begin{tabular}{|lcc|} \hline \multicolumn{1}{|c}{ Shift } & \begin{tabular}{c} Unsafe \\ Conditions \end{tabular} & \begin{tabular}{c} Human \\ Error \end{tabular} \\ \hline Day & 3%3 \% & 35%35 \% \\ Evening & 6%6 \% & 23%23 \% \\ Graveyard & 1%1 \% & 32%32 \% \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. Total number of accidents is 300.
2. Percentages can be converted to actual counts by multiplying with the total number of accidents.
3. Probabilities are calculated by dividing the number of favorable outcomes by the total number of outcomes.

STEP 2

1. Calculate the number of accidents for each condition and shift combination.
2. Calculate the probability for each specific condition or shift as requested in parts (a) through (d).

STEP 3

Calculate the number of accidents that occurred during the day shift due to unsafe conditions.
Day Shift, Unsafe Conditions=0.03×300=9 \text{Day Shift, Unsafe Conditions} = 0.03 \times 300 = 9

STEP 4

Calculate the number of accidents that occurred during the day shift due to human error.
Day Shift, Human Error=0.35×300=105 \text{Day Shift, Human Error} = 0.35 \times 300 = 105

STEP 5

Calculate the number of accidents that occurred during the evening shift due to unsafe conditions.
Evening Shift, Unsafe Conditions=0.06×300=18 \text{Evening Shift, Unsafe Conditions} = 0.06 \times 300 = 18

STEP 6

Calculate the number of accidents that occurred during the evening shift due to human error.
Evening Shift, Human Error=0.23×300=69 \text{Evening Shift, Human Error} = 0.23 \times 300 = 69

STEP 7

Calculate the number of accidents that occurred during the graveyard shift due to unsafe conditions.
Graveyard Shift, Unsafe Conditions=0.01×300=3 \text{Graveyard Shift, Unsafe Conditions} = 0.01 \times 300 = 3

STEP 8

Calculate the number of accidents that occurred during the graveyard shift due to human error.
Graveyard Shift, Human Error=0.32×300=96 \text{Graveyard Shift, Human Error} = 0.32 \times 300 = 96

STEP 9

Calculate the total number of accidents that occurred during the evening shift.
Evening Shift, Total=18+69=87 \text{Evening Shift, Total} = 18 + 69 = 87

STEP 10

Calculate the probability that an accident occurred during the evening shift.
P(Evening Shift)=87300=0.29 P(\text{Evening Shift}) = \frac{87}{300} = 0.29

STEP 11

Calculate the total number of accidents that occurred due to human error.
Human Error, Total=105+69+96=270 \text{Human Error, Total} = 105 + 69 + 96 = 270

STEP 12

Calculate the probability that an accident occurred due to human error.
P(Human Error)=270300=0.9 P(\text{Human Error}) = \frac{270}{300} = 0.9

STEP 13

Calculate the total number of accidents that occurred due to unsafe conditions.
Unsafe Conditions, Total=9+18+3=30 \text{Unsafe Conditions, Total} = 9 + 18 + 3 = 30

STEP 14

Calculate the probability that an accident occurred due to unsafe conditions.
P(Unsafe Conditions)=30300=0.1 P(\text{Unsafe Conditions}) = \frac{30}{300} = 0.1

STEP 15

Calculate the total number of accidents that occurred during either the evening or the graveyard shift.
Evening or Graveyard Shift, Total=87+(3+96)=186 \text{Evening or Graveyard Shift, Total} = 87 + (3 + 96) = 186

STEP 16

Calculate the probability that an accident occurred during either the evening or the graveyard shift.
P(Evening or Graveyard Shift)=186300=0.62 P(\text{Evening or Graveyard Shift}) = \frac{186}{300} = 0.62
Solution: (a) The probability that the accident occurred on the evening shift is 0.290.29.
(b) The probability that the accident occurred due to human error is 0.90.9.
(c) The probability that the accident occurred due to unsafe conditions is 0.10.1.
(d) The probability that the accident occurred on either the evening or the graveyard shift is 0.620.62.

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