5. Binomial Distribution & Discrete Random Variables

A baker wants to predict how many customers will enter their bakery. Determine which probability distribution they should use given the following information.

(A) There is a 10% chance that any one person who walks by will enter the bakery and 20 people walk by.

A baker wants to predict how many customers will enter their bakery. Determine which probability distribution they should use given the following information.

(B) On average, 2 customers come into the bakery every 15 minutes.

A baker wants to predict how many customers will enter their bakery. On average, 2 customers come into the bakery every 15 minutes. Find the probability that:

(A) Exactly 4 customers will enter the bakery in a random 15 min period.

A baker wants to predict how many customers will enter their bakery. On average, 2 customers come into the bakery every 15 minutes. Find the probability that:

 (B) 4 or fewer customers enter the bakery in a random 15 min period.

"Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Hurricanes The mean number of hurricanes to strike the U.S. mainland per year from 1851 through 2020 was about 1.8. Find the probability that the number of hurricanes striking the U.S. mainland in any given year from 1851 through 2020 is (a) exactly one, (b) at most one, and (c) more than one. (Source: National Oceanic & Atmospheric Administration)"

"Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

Typographical Errors A newspaper finds that the mean number of typographical errors per page is four. Find the probability that the number of typographical errors found on any given page is (a) exactly three, (b) at most three, and (c) more than three."

"[DATA] Putting It Together: The V-2 Rocket in London In Thomas Pynchon’s book Gravity Rainbow, the characters discuss whether the Poisson probabilistic model can be used to describe the locations that Germany’s feared V-2 rocket would land in. They divided London into 0.25-km2 regions. They then counted the number of rockets that landed in each region, with the following results:

a. Estimate the mean number of rocket hits in a region by computing . Round your answer to four decimal places."

"[DATA] Putting It Together: The V-2 Rocket in London In Thomas Pynchon’s book Gravity Rainbow, the characters discuss whether the Poisson probabilistic model can be used to describe the locations that Germany’s feared V-2 rocket would land in. They divided London into 0.25-km2 regions. They then counted the number of rockets that landed in each region, with the following results:

d. A total of n = 576 rockets was fired. Determine the expected number of rocket hits, E, by computing E=np where p is the probability of observing that particular number of hits in the region."