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
