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 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.

A quality control inspector at a textile factory is examining long rolls of fabric for defects. The inspector knows from past experience that, on average, there are 0.5 defects per meter of fabric. What is the probability that the inspector finds 0 defects in any given meter of fabric?

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 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.