Salmonellosis outbreak. Improperly handled or undercooked poultry and eggs are the most frequent cause of salmonella food poisoning. Salmonellosis can be deadly, although most individuals recover on their own. Cases must be reported to the CDC, where they are closely monitored. The average number of salmonellosis cases per month in South Dakota is 1.6. Let X be the monthly count of salmonellosis cases in South Dakota. a) Identify an appropriate probability distribution model for X. b) Find the mean and standard deviation of X. Round to 2 decimal places mean = standard deviation = c) The mean and standard deviation of salmonellosis cases in South Dakota over a six month period are mean =

a) Poisson probability distribution model

b)

Mean=1.6.

Standard deviation=1.26.

c)

Mean=9.6.

Standard deviation=3.10.

Step-by-step explanation:

a)

The number of cases of salmonellosis has a rare frequency of occurring and also we can assume that trails are independent. So, the X the monthly count of salmonellosis cases in South Dakota is a Poisson random variable.

Thus, the appropriate probability distribution model for X is the Poisson probability distribution model.

b)

The mean and variance of the Poisson probability distribution model is μ the average number of salmonellosis cases per month in South Dakota.

Mean=E (x) = μ=1.6

Standard deviation=√V (x) = √μ=√1.6=1.26

c)

The average number of salmonellosis cases per month = 1.6

The average number of salmonellosis cases over 6 months=6*1.6=9.6

The mean and variance of the Poisson probability distribution model is μ the average number of salmonellosis cases over 6 months in South Dakota.

Mean=E (x) = μ=9.6

Standard deviation=√V (x) = √μ=√9.6=3.10