Answer:
Hence, the required probability is [tex]0.0004[/tex].
Given :
[tex]90\%[/tex] of the booked passengers arrive for the flight.
Number of booked passengers n [tex]=318[/tex]
Number of seats available x [tex]=310[/tex]
To find :
The probability that if the company books 318 persons.
Explanation :
[tex]n=318,x=310[/tex]
[tex]P=0.09(90\%)[/tex]
Mean [tex]\bar{x}=nP[/tex]
[tex]\Rightarrow \bar{x}=318\times 0.09[/tex]
[tex]\Rightarrow \bar{x}=28.62[/tex]
Standard deviation [tex]\sigma =\sqrt{nPq[/tex] where [tex]q=1-P[/tex]
[tex]\Rightarrow \sigma =\sqrt{318\times 0.09\times 0.91}[/tex]
[tex]\Rightarrow \sigma=\sqrt{26.0442}[/tex]
[tex]\Rightarrow \sigma =5.1033[/tex]
Required probability[tex]=P(x>310)[/tex]
[tex]=1-P(x<310)[/tex]
[tex]=1-P(\frac{x-\bar{x}}{\sigma}<\frac{310-28.62}{5.1033})[/tex]
[tex]=1-P(z<55.1368)[/tex]
[tex]=1-0.9995[/tex]
[tex]=0.0004[/tex]
