A student working on a transportation engineering project analyzes traffic flow at an intersection for 20 min. From past data, the average # of cars per minute is 17.6.
(B) Find the probability that the student observes 350 or more cars total.

A financial analyst is assessing the risk of credit defaults in a large bond portfolio. The portfolio contains 2,000 corporate bonds, & the probability of any one bond defaulting in a year is 0.002.

(A) Can the # of bonds which will default be approximated using the Poisson distribution? If so, find $\lambda$.

A financial analyst is assessing the risk of credit defaults in a large bond portfolio. The portfolio contains 2,000 corporate bonds, & the probability of any one bond defaulting in a year is 0.002.

(B) Use the Poisson distribution to estimate the probability that more than 5 bonds default in a year.

A financial analyst is assessing the risk of credit defaults in a large bond portfolio. The portfolio contains 2,000 corporate bonds, & the probability of any one bond defaulting in a year is 0.002.

(C) The analyst considers any probabilities less than 5% to be significant. If more than 5 bonds default in a year, should the analyst be concerned? 

A student working on a transportation engineering project analyzes traffic flow at an intersection for 20 min. From past data, the average # of cars per minute is 17.6.

(A) What is the expected number of cars in the entire 20 min period?

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 small electronics retailer tracks the number of customers who arrive to purchase replacement phone chargers. Based on historical data, the store finds that, on average, 3 customers per day buy a charger. The store manager wants to use this information to optimize inventory decisions and reduce the risk of stockouts.

(A) Find the probability that 5 customers buy a charger in a given day.

A small electronics retailer tracks the number of customers who arrive to purchase replacement phone chargers. Based on historical data, the store finds that, on average, 3 customers per day buy a charger. The store manager wants to use this information to optimize inventory decisions and reduce the risk of stockouts.

(B) If the store stocks 5 chargers per day, find the probability that they will have inventory remaining on a given day.