Question

Need some correction about this Probability problem:
The number of defective products produced by a factory in one day is modeled by a random variable with density Poisson(k;14.3).

What is the probability that at least 14 defective products are produced in a single day?

Answer 1

the answer support to be 0.42202
or
0.5670

Answer 2

which formula should I use \[1-\sum_{0}^{13} e^{-\lambda} \frac{ \lambda^n }{ n! }\]
or
\[\sum_{0}^{13} e^{-\lambda} \frac{ \lambda^n }{ n! }\]
for this problem

Answer 3

what does "at least" mean?

Answer 4

i guess is mean aprox less than and equal to 14 ?

Answer 5

at least14 ... the least is 14

you must be at least this tall, to ride this ride ... anyone shorter cannot get in

you must be at least this age to see this movie ... anyone younger cannot get in

you have to go at least this speed to qualify for the race ... any slower does not get in.

at least 14, includes: 14,15,16,17,18,...

Answer 6

i see

Answer 7

that going to be infinity with 14

Answer 8

P(0)+P(1)+...+P(13)+P(14)+P(15)+... = 1

P(14)+P(15)+... = 1 - [P(0)+P(1)+...+P(13)]

Answer 9

1-P(X<= 13) = 1-[ P(X=0) + P(X=1) + ... + P(X=13)]

Answer 10

do that mean both are the same, must be equal to 1

Answer 11

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

P(X<=13) + P(X>=14) = 1

you want P(X>=14) = 1- P(X<=13)