SOLUTION: . Assuming that a plane makes a safe flight if at least half the numbers of engine run. Find whether a 6 engine plane or a 4 engine plane has a higher probability of successful fli

Question 898153: . Assuming that a plane makes a safe flight if at least half the numbers of engine run. Find whether a 6 engine plane or a 4 engine plane has a higher probability of successful flight.
ii) The marks obtained in Probability & Statistics by 1000 students is normally distributed is normally distributed with mean 78% and standard deviation 11%. Determine (a). How many students got the marks above 90%
(b).What was the highest mark obtained by the lowest of 10% of the students
(c).Within what limits did the middle of 90% of the students lie.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Assuming that a plane makes a safe flight if at least half the numbers of engine run. Find whether a 6 engine plane or a 4 engine plane has a higher probability of successful flight.
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Assuming each engine has a 50% chance of failing,
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P(4 engine plane safe) = 1 - P(3 engines fail) = 1-(1/8) = 7/8
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P(6 engine plane safe) = 1 - P(4 engines fail) = 1-(1/16) = 15/16
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Ans:: 6 is safer
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ii) The marks obtained in Probability & Statistics by 1000 students is normally distributed is normally distributed with mean 78% and standard deviation 11%. Determine (a). How many students got the marks above 90%
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z(90) = (90-78)/11 = 12/11
P(x > 90) = P(z > 12/11) = normalcdf(12/11,100) = 0.1377
Ans: 0.1377*1000 = 138 students (when rounded up)
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(b).What was the highest mark obtained by the lowest of 10% of the students
Find the z-value with a left tail of 10%::
invNorm(0.10) = -1.2816
Find the corresponding "x" value::
x = -1.2816*11 + 78 = 63.9
Ans:: 63.9%
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(c).Within what limits did the middle of 90% of the students lie.
Find the z-value with a left tail of 5%::
invNorm(0.05) = 1.645
Find the corresponding x-value::
x = -1.645*11 + 78 = 59.9
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Lower Limit = 59.9%
By symmetry the upper limit is 1.645*11+78 = 96.1
Upper Limit = 96.1%
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Cheers,
Stan H.
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