(7 points) Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a two-minute phone call, what is the probability that at least 1 car arrives during the call

The probability that at least 1 car arrives during the call is 0.9306

Step-by-step explanation:

Cars arriving according to Poisson process - 80 Cars per hour

If the attendant makes a 2 minute phone call, then effective λ = 80/60 * 2 = 2.66666667 = 2.67   X ≅ Poisson (λ = 2.67)

Now, we find the probability: P(X≥1)

P(X≥1) = 1 - p(x < 1)

P(X≥1) = 1 - p(x=0)

P(X≥1) = 1 - [ (e^-λ) * λ^0] / 0!

P(X≥1) = 1 - e^-2.67

P(X≥1) = 1 - 0.06945

P(X≥1) = 0.93055

P(X≥1) = 0.9306

Thus, the probability that at least 1 car arrives during the call is 0.9306.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

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