High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. Cockpit noise in a jet aircraft is mostly due to airflow at hundreds of miles per hour. This 3 × 3
- i. P(B)
- ii. P(L)
- iii. P(H | C)
- iv. P(H | D)
- v. P(L and B)
- vi. P(L and C)
a.
Calculate each probability (i-vi) and explain it meaning in words.
Answer to Problem 96CE
i. The probability
ii. The probability
iii. The probability
iv. The probability
v. The probability
vi. The probability
Explanation of Solution
Calculation:
The given table shows that cockpit noise levels in the jet aircraft.
The given contingency table is,
Flight Phase | ||||
Noise Level | Climb (B) | Cruise (C) | Descent (D) | Row Total |
Low (L) | 6 | 2 | 6 | 14 |
Medium (M) | 18 | 3 | 8 | 29 |
High (H) | 1 | 3 | 14 | 18 |
Column Total | 25 | 8 | 28 | 61 |
For (i)
The formula for finding the probability
Substitute 25 for ‘Frequency for the class B’ and 61 for ‘Total frequencies in the distribution’
Therefore, the probability
For (ii)
The formula for finding the probability
Substitute 14 for ‘Frequency for the class L’ and 61 for ‘Total frequencies in the distribution’
Therefore, the probability
For (iii)
The formula for finding the probability
Substitute 3 for ‘Frequency for the class H and C’ and 8 for ‘Frequency for the class C’,
Therefore, the probability
For (iv)
The formula for finding the probability
Substitute 14 for ‘Frequency for the class H and D’ and 28 for ‘Frequency for the class D’,
Therefore, the probability
For (v)
The formula for finding the probability
Substitute 6 for ‘Frequency for the class L and B’ and 61 for ‘Total frequencies in the distribution’,
Therefore, the probability
For (vi)
The formula for finding the probability
Substitute 2 for ‘Frequency for the class L and C’ and 61 for ‘Total frequencies in the distribution’,
Therefore, the probability
b.
Check whether there is evidence that noise level depends on flight phase. Also, explain the reason.
Answer to Problem 96CE
Yes, there is evidence that noise level depends on flight phase because
Explanation of Solution
Calculation:
Special law of multiplication:
If two events A and B are independent, then
Consider noise level as High and flight phase type as cruise.
The formula for checking independence is,
Here, it is observed that
c.
Identify the ambient noise is an ergonomic issue.
Explanation of Solution
Answers may vary: One of the answers is given below:
Some of the ambient noises are an ergonomic issues are,
- • The noise from the heavy machines running in a factory.
- • The excess sound created by vehicles in the traffic signals.
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APPLIED STAT.IN BUS.+ECONOMICS
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