Question

Suppose the number of cars pulling into a certain convenience store between 2:00 and 3:00 am on weeknights approximately follows a Poisson distribution with X = 2.8 On a randomly selected weeknight, what is the probability fewer than 1 cars pull in between 2:00 and 3:00 am? Round your answer to at least 3 decimal places. Number

Answer 1

1)

Here, λ = 2.8 and x = 1
As per Poisson's distribution formula P(X = x) = λ^x * e^(-λ)/x!

We need to calculate P(X < 1).
P(X <1) = (2.8^0 * e^-2.8/0!)
P(X < 1) = 0.0608
P(X < 1) = 0.061

2)

a)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (3.4 - 3.2)/(0.89/sqrt(73))
z = 1.920

b)

P-value = 0.027

c)

1)
yes

2)

yes