Answer to Question #126427 in Statistics and Probability for Sujatha

Question

This is the main question has 5 parts-
At Penna Airport the probability P(A) that all passengers arrive on time for a flight is 0.70. The probability P(D) that departs on time is 0.85.
a) The probability that all passengers arrive on time for a flight and it departs on time is 0.65. b) Show that event A & D are not independent. Find P(A intersection D').
Given that all passengers for a flight arrive on time, c) Find the probability that the flight deos not depart on time.
The number of hours that pilots fly per week is normally distributed with mean of 25 hours and standard deviation. 90% of pilots fly less than 28 hours in week.
d) Find the value of standard deviation
All flights have two pilots
e) Find the percentage of flights where both pilots flew more than 30 hours last week

Answer 1

The probability that all passengers arrive on time for a flight and it departs on time is 0.65 and it is not equal to P(A)*P(D) (0.85*0.7=0.595) so A & D are not independent

P(A∩D)=P(D)P(A|D)=0.70*0.65=0.455

 Find the probability that the flight deos not depart on time P=1-0.85=0.15

μ=25

P(x<28)=0.9, z-value=1.28

1.28=(28-25)/σ

σ =3/1.28=2.34

P(x>30)=1-P(x<30)

P(x<30), z=(30-25)/2.34=2.14,using table p =0.98382

P(x>30)=0.01618

for both pilots P=0.01618²=0.0002617924