Question

According to the Bureau of Transportation​ Statistics, 81.9​% of American Airlines flights were on time in 2017. Assume this percentage still holds true for American Airlines. For the next 46 flights from American​ Airlines, use the normal approximation to the binomial distribution. Determine the probability that 34, 35, 36, or 37 flights will arrive on time.

Answer 1

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Answer:

Sample size , n = 46
Probability of an event of interest, p =   0.819                              
we need to calculate probability for ,                                  
34 ≤ X ≤    37   
Mean = np = 37.674   
std dev ,σ=√np(1-p)=   2.61132   
                                  
P ( 34 ≤ X ≤    37 ) = P ( 33.5 ≤ Xnormal ≤   37.5   )  
Z1 =   (X1normal - µ ) / σ =   -1.5984251   
Z2 =   (X2 normal- µ ) / σ = -0.066632958   
                                  
P (    -1.5984251 ≤ Z ≤   0.066632958 )                   

0.4185