Question

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 1.69. Let X be the monthly count of salmonellosis cases in South Dakota.Let X be the monthly count of salmonellosis cases in South Dakota.b) Find the mean and standard deviation of X. Round to 2 decimal placesc) The mean and standard deviation of salmonellosis cases in South Dakota over a six month period are

Answer 1

Answer:

Step-by-step explanation:

Let X be the monthly count of salmonellosis cases in South Dakota.

And X has Poisson(A 1.62)

E(X) = \lambda = 1.62

Var(X) = \lambda = 1.62

Standard Deviation (X) = \sqrt{\lambda} = \sqrt{1.62} = 1.27

c)

Mean of salmonellosis cases in South Dakota over a six month period is = 6*1.62 = 9.72

standard deviation of salmonellosis cases in South Dakota over a six month period is = 6*1.27 = 7.62

Answer 2

Answer:

A. Mean= 1.69

Standard deviation = 1.3

B. mean= 1.69

Standard deviation= 0.02

Step-by-step explanation:

A. FIND THE MEAN AND STANDARD DEVIATION;

Since 1.69 is the average number of salmonellosis cases per month in South Dakota. Therefore

Mean = 1.69

This mean is equal to the variance because we are not given a range of number to find the standard deviation.

Mean = variance

Standard deviation= √variance =√mean

Therefore;

Standard deviation = √1.69 = 1.3

B. FIND THE MEAN AND STANDARD DEVIATION OVER SIX MONTHS PERIOD;

Mean = 1.69

STANDARD DEVIATION:

Step 1: find the six values of the mean

Mean = sum of values÷ number of occurrence

1.69= sum of values / 6

Sum of values = 10.14

Let's assume the six numbers to be

1.66 + 1.67 + 1.68 + 1.70 + 1.71 + 1.72 = 10.14

Step2: subtract the mean from the value and square

(1.66 - 1.69)^2 = 0.0009

(1.67 - 1.69)^2= 0.0004

(1.68 - 1.69)^2 = 0.0001

(1.70 - 1.69)^2 = 0.0001

(1.71 - 1.69)^2 = 0.0004

(1.72 - 1.69)^2 = 0.0009

STEP3: add all the results in step 2

0.0009 + 0.0004 + 0.0001 + 0.0001 + 0.0004 + 0.0009 = 0.0028

STEP4: Find variance

0.0028 ÷ 6 = 0.0004667

STEP5 : Find standard deviation;

Standard deviation= √0.0004667 =

0.0216

To two significant figure, Therefore;

standard deviation= 0.02