14. The number of cases of tetanus reported in the United States during a in 198

Question

14. The number of cases of tetanus reported in the United States during a in 1989 bas a Poisson distribution with parameter i 4518) (a) What is the probability that exactly one case of tetanus will be reported during a given month? (b) What is the probability that at most two cases of tetanus will be reported? (c) What is the probability that four or more cases will be reported? d) What is the mean number of cases of tetanus reported in a one-month period? What is the standard deviation? 15. In a particular county, the average number of suicides reported each month is 2.75 1131. Assume that the number of suicides follows a Poisson distribution. (a) What is the probability that no suicides will be reported during a given month? (b) What is the probability that at most four suicides will be reported? (e) What is the probability that six or more suicides will be reported 16. Let X be a random variable that represents the number of infants in a group of 2000 who die before reaching their first birthdays. In the United States, the probability that a child dies during his or her first year of life is 0.0085 (141 (a) What is the mean number of infants who would die in a group of this size? (b) What is the probability that at most five infants out of 2000 die in their first year of life? What is the probability that between 15 and 20 infants die in their first year of life? (e)

Explanation / Answer

Solution14:

X follows poisson distribution

mean=4.5

SOlution14a:

P(X=1)

=e^-lamba *lamba^x/x!

=e^-4.5*4.5^1/1!

=0.04999

Solutionb:

P(X<=2)

=P(X=0)+P(X=1)+P(X=2)

=0.0111+0.05+0.1125

=0.1736

Solutionc:

P(X>=4)

=1-P(X<4)

=1-P(X<=3)

=1-0.3423

=0.6577

Solutiond:

mean=lamba=4.5

for possion distribution mean and varaince are equal

varinace=4.5

standard deviation=sqrt(variance)=

=sqrt(4.5)

= 2.12132

standard deviation=2.12132

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