Answer:
(a) 0.139258
(b) 0.0064827
Step-by-step explanation:
Let the probability that each member makes a correct decision be
and the probability that each member makes an incorrect decision be
.
From the question, ![p = 0.7](https://tex.z-dn.net/?f=p%20%3D%200.7)
p and q are mutually exclusive. Hence,
![p+q = 1](https://tex.z-dn.net/?f=p%2Bq%20%3D%201)
![q = 1 - p=1-0.7 = 0.3](https://tex.z-dn.net/?f=q%20%3D%201%20-%20p%3D1-0.7%20%3D%200.3)
(a) For majority rule, it means at least 4 members decisions are taken. Taking "C" to mean "correct" and "I" to mean "incorrect", we could have 4C against 3I, 5C against 2I, 6C against 1I and 7C against 0I.
The probability of the correct decision being made is
![P(\ge\text{4C}) = P(\text{4C and 3I}) + P(\text{5C and 2I}) +P(\text{6C and 1I}) +P(\text{7C and 0I})](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20P%28%5Ctext%7B4C%20and%203I%7D%29%20%2B%20P%28%5Ctext%7B5C%20and%202I%7D%29%20%20%20%2BP%28%5Ctext%7B6C%20and%201I%7D%29%20%2BP%28%5Ctext%7B7C%20and%200I%7D%29)
![P(\ge\text{4C}) = (0.7^4\times0.3^3)+(0.7^5\times0.3^2)+(0.7^6\times0.3^1)+(0.7^7\times0.3^0)](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20%280.7%5E4%5Ctimes0.3%5E3%29%2B%280.7%5E5%5Ctimes0.3%5E2%29%2B%280.7%5E6%5Ctimes0.3%5E1%29%2B%280.7%5E7%5Ctimes0.3%5E0%29)
![P(\ge\text{4C}) = 0.0064827 + 0.0151263 + 0.0352947 + 0.0823543 = 0.139258](https://tex.z-dn.net/?f=P%28%5Cge%5Ctext%7B4C%7D%29%20%3D%20%200.0064827%20%2B%200.0151263%20%2B%200.0352947%20%2B%200.0823543%20%3D%200.139258)
(b) ![P(\text{exactly 4C}) = P(\text{4C and 3I}) = 0.7^4\times0.3^3 = 0.0064827](https://tex.z-dn.net/?f=P%28%5Ctext%7Bexactly%204C%7D%29%20%3D%20P%28%5Ctext%7B4C%20and%203I%7D%29%20%3D%200.7%5E4%5Ctimes0.3%5E3%20%3D%200.0064827)
Answer:
Let say 75% of cars older than age = Y years
than 25 % cars of age less than Y Years
Z score corresponding to 25 % = -0.674
Z score = (Value - Mean) /SD
Value = Y
Mean = 8
SD = 3.2
Z score = -0.674
-0.674 = (Y - 8)/3.2
=> Y =5.84 Years
=> Y ≈ 5.9 Years
Approximately 75% of cars driven by company employees are older than about 5.9 years
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Use technology or the z-distribution table on pages A-1 to A-2 in the ...
Answer:
48
Step-by-step explanation:
The LCM of 12 and 16 is 48.
12*4= 48
16*4= 48
Answer:
The answer is B
Step-by-step explanation:
22 runs into 464 with this many out comes
Multiply both sides by 17:
![-7 \cdot 17 = 11z](https://tex.z-dn.net/?f=%20-7%20%5Ccdot%2017%20%3D%2011z%20)
Evaluate the left hand side:
![-119 = 11z](https://tex.z-dn.net/?f=%20-119%20%3D%2011z%20)
Finally, divide both sides by 11:
![\displaystyle z = -\dfrac{119}{11}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20z%20%3D%20-%5Cdfrac%7B119%7D%7B11%7D%20)