On an average, a clothing store gets 120 customers per day. Let the random variable be X~P (120). What is the probability of getting 150 customers in one day?Question 4Answera.0.05b.0.0010c.0.2
Question
On an average, a clothing store gets 120 customers per day. Let the random variable be X~P (120). What is the probability of getting 150 customers in one day?Question 4Answera.0.05b.0.0010c.0.2
Solution
The question is asking for the probability of getting 150 customers in one day, given that the average number of customers per day is 120. This is a Poisson distribution problem.
The formula for the Poisson probability is:
P(x; μ) = (e^-μ) * (μ^x) / x!
where:
- P(x; μ) is the Poisson probability,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- μ is the average number of successes that result from the experiment (in this case, 120 customers),
- x is the actual number of successes that result from the experiment (in this case, 150 customers).
Substituting the given values into the formula, we get:
P(150; 120) = (e^-120) * (120^150) / 150!
Calculating this will give us the probability of getting 150 customers in one day. This calculation might be complex and require the use of a calculator or software that can handle large numbers and factorials.
Please note that the options provided (a.0.05, b.0.0010, c.0.2) might not match the actual calculated result.
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