shoppers enter hamilton place mall at an average of 120 per hour what is the probability that at least 20 shoppers

This question is incomplete, the complete question is;

Shoppers enter Hamilton place mall at an average of 120 per hour

what is the probability that at least 20 shoppers but no more than 23 shoppers enter the  mall between noon and 12:30 p.m.?

Answer:

the probability that at least 20 shoppers but no more than 23 shoppers enter the  mall between noon and 12:30 p.m

is 4.20787 × 10⁻⁸ ≈ 0.0000000420787  

Step-by-step explanation:

the probability that at least 20 shoppers but no more than 23 shoppers enter the  mall between noon and 12:30 p.m;

interval between noon and 12:30 is 30min

now the shoppers enter an average of  [(120 × 30) / 60] = 60 per 30min

so

P( 20 ≤ X ≥ 23 ) = P( X=20 ) + P( X=21 ) + P( X=22 ) + P( X=23 )

= [(e⁻⁶⁰(60)²⁰) / 20!] + [(e⁻⁶⁰(60)²¹) / 21!] + [(e⁻⁶⁰(60)²²) / 22!] + [(e⁻⁶⁰(60)²³) / 23!]

= [1.3159 × 10⁻⁹] + [3.7598 × 10⁻⁹] + [1.0254 × 10⁻⁸] + [2.6749 × 10⁻⁸]

= 4.20787 × 10⁻⁸ ≈ 0.0000000420787  

therefore the probability that at least 20 shoppers but no more than 23 shoppers enter the  mall between noon and 12:30 p.m is 4.20787 × 10⁻⁸ ≈ 0.0000000420787  

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