A new shopping mall is being built with 333 stores and 7 movie theatres. The number of movie theatres was based on statistics that 3.7% of mall goers like to watch a movie after shopping. Now the building is complete and the theatres are almost complete too. What is the probability that the 7 theatres won't be enough for the 333 stores and more will be needed to satisfy the demand?
a) The probability that the 333 stores will need more than 7 theatres to satisfy the demand is ____ . (Round to three decimal places as needed.)
Using binomial distribution,
= n * p = 333 * 0.037 = 12.321
= n * p * q = 333 * 0.037 * (1 - 0.037) = 3.4446
Using continuity correction ,
P(x > 7.5) = 1 - P(x < 7.5)
= 1 - P((x - ) / < (7.5 - 12.321) / 3.4446)
= 1 - P(z < -1.40)
Probability = 0.919
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