Answer to Question #104170 in Statistics and Probability for Katenda

Question

The average number of adults with ASD consulting with a Neuropsychologist per day is
Poisson distributed with the mean of 1.5. Use this information to answer questions 7 to 9.

Question 7

What is the probability that on any given day a Neuropsychologist will consult with only 1 adult with ASD?
(1) 0.3230
(2) 0.3452
(3) 0.2510
(4) None of the above.
(5) Need more information to calculate the probability

Question 8

What is the probability that on any given day a Neuropsychologist will consult with at least 7 adults with ASD?
(1) 0.0013
(2) 0.0009
(3) 0.0008
(4) 0.0006
(5) None of the above.

Question 9

What is the variance of the number of adults with ASD consulting with a Neuropsychologist on any given day?
(1) 0
(2) 1.5
(3) 3
(4) 4.5
(5) None of the above.

Answer 1

Question 7

mean= 1.5

$P(=1)=e^{-1.5}×1.5=0.334695$

Similarly, =POISSON.DIST(1,1.5,FALSE) yields 0.334695.

Answer is (4).

Question 8

$P(\geq7)=1-P(\le6)$

The Excel formula =1-POISSON.DIST(6,1.5,TRUE) yields 0.000926.

Answer is (2).

Question 9

The variance of a poisson distribution is equal to mean. Variance in this case is 1.5. Answer is (2).