Question

1. An automobile manufacturer has determined that 33% of all gas tanks that were installed on its 2015 compact model are defective. If 16 of these cars are independently sampled, what is the probability that at least 6 of the sample need new gas tanks?

2. Use the Poisson Distribution Formula to find the indicated probability: Last winter, the number of potholes that appeared on a 9.0-mile stretch of a particular road followed a Poisson distribution with a mean of 34.5. Find the probability that exactly six potholes can be found on any mile-and-a-half portion of this road.

3. The mean number of homicides per year in one city is 106.6. Use a Poisson distribution to find the probability that in a given week there will be fewer than three homicides. (HINT: Assume a year is exactly 52 weeks.)

4. Use the Poisson Distribution Formula to find the indicated probability.

For a certain type of fabric, the average number of defects in each square foot of fabric is 4.4. Find the probability that a randomly selected square foot of the fabric will contain at least two defects.Round your answer to four decimal places. Hint: The answer is the complement of the probability that there is at most 1 defect.

5. In one town, the number of burglaries in a week has a Poisson distribution with mean μ = 5.5. Let variable x denote the number of burglaries in this town in a randomly selected month. Find the smallest usual value for x. Round your answer to three decimal places. (HINT: Assume a month to be exactly 4 weeks)

I know the answers to these, I just want to know how to calculate. Thank you!

Answer 1