Question

1.According to the Port Authority of New York and New Jersey, 81.9% of New Jersey Transit trains ran  on time during 2018.  Assume that this percentage still holds true.  Using the normal approximation to the binomial distribution, determine the probability that the next 30 trains

a.   a. Fewer than 22 trains will run on time

b.   b.Exactly 26 trains will run on time

c.       c. 21,22,23, or 24 will run on time.

2. Consider that the hits on the Amazon website follow  the exponential distribution with a mean time of 2.7 minutes.

a.       a. What is the probability that the next hit on Amazon will occur in the next 5 minutes.

b.      b. What is the probability that the next hit will be between the next 2 to 6 minutes?

c.       c. What is the probability that the next hit will occur after the next 3 minutes?

3. Whole Foods has 18 two-liter bottles of a new Probiotic drink on the shelf, 4 of which had exceeded the shelf-life date.  You randomly select 3 bottles of the new drink without checking the expiration date.  Determine the probability that:

a.       a. None of the bottles have exceeded the expiration date.

b.      b. At least two bottles had exceeded the expiration date.

c.       c. Calculate the mean and standard deviation of this distribution.

Answer 1

1:

(a)

Using continuity correction factor the probability that fewer than 22 trains will run on time is

P(X< 22) = P(X < 22-0.5) = P(X < 21.5)

(b)

Using continuity correction factor the probability that exactly 26 trains will run on time is

P(X = 26) = P(26 -0.5 < X < 26+0.5) = P(25.5 < X < 26.5)

(c)

Using continuity correction factor the probability that 21,22,23, or 24 will run on time is

P(21 <= X <= 24) = P(21 -0.5 < X < 24+0.5) = P(20.5 < X < 24.5)