Question

3. The flight time from Raleigh Durham International Airport (RDU) to Hartsfield International Airport (ATL) is normally distributed with a mean of 89 min and a standard deviation of 4 min.
(A) What is the probability a flight takes at least 96 minutes? (9 points)
(B) What is the probability a flight takes between 93 and 97 minutes? (10 points)
(C) Ten percent of flights will take more than how many minutes? (10 points)
(D) There are 13 flights on a given day from RDU to ATL. What is the mean of the sampling distribution of these flights? Label your answer with correct statistical notation. (4 points)
(E) What is the standard error of the mean of these 13 flights? Label your answer with correct statistical notation. (4 points)
(F) What is the probability the mean time for these 13 flights is less than 90 minutes? (8 points)

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Answer 1

a)

µ =    89                  
σ =    4                  
                      
P ( X ≥   96.00   ) = P( (X-µ)/σ ≥ (96-89) / 4)              
= P(Z ≥   1.750   ) = P( Z <   -1.750   ) =    0.0401   (answer)

b)

µ =    89                              
σ =    4                              
we need to calculate probability for ,                                  
P (   93   < X <   97   )                  
=P( (93-89)/4 < (X-µ)/σ < (97-89)/4 )                                  
                                  
P (    1.000   < Z <    2.000   )                   
= P ( Z <    2.000   ) - P ( Z <   1.000   ) =    0.9772   -    0.8413   =    0.1359

c)

µ=   89                  
σ =    4                  
proportion=   0.9                  
                      
Z value at    0.9   =   1.28   (excel formula =NORMSINV(   0.9   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   1.28   *   4   +   89  
X   =   94.13   (answer)          

d)

mean of the sampling distribution of these flights

= 89

e)

Standard error = 4/ sqrt(13)

= 1.1094

f)

µ =    89      
σ =    1.109400392      
          
P( X ≤    90   ) = P( (X-µ)/σ ≤ (90-89) /1.10940039245046)  
=P(Z ≤   0.901   ) =   0.8163

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