Question

about 50% of patients bach with a certain cancer recover fully. a hospital is curing for five patients born with the alment. the random variable represents the number of tumes that recover fully. describe whether the experiment is a binomial experiment, is the experiment a binomial experiment?
no
yes
what is a success in this experiment?
every recovers
every doesnt recover
this is not a binomial experiment
specify the value of n. select the correct choice below and fill in any answer boxes in your choice.
a. ( n = )
b. this is not a binomial experiment.
specify the value of p. select the correct choice below and fill in any answer boxes in your choice.
a. ( p = )
b. this is not a binomial experiment.
specify the value of q. select the correct choice below and fill in any answer boxes in your choice.
a. ( q = )
b. this is not a binomial experiment.
list the possible values of the random variable x.
( x = 0,1,2,3,4 )
( x = 0,1,2,3,5 )
( x = 1,2,3,4,5 )
this is not a binomial experiment

Explanation:

• Is the experiment a binomial experiment?
• A binomial experiment has the following characteristics: a fixed number of trials (\(n\)), each trial has only two possible outcomes (success - failure), the probability of success (\(p\)) is constant for each trial, and the trials are independent.
• Here, the number of trials \(n = 5\) (five patients), each patient either recovers fully (success) or not (failure), the probability of success \(p=0.5\) (since about \(50\%\) of patients with a certain ailment recover fully), and the recovery of one patient does not affect the recovery of another (independent trials). So, it is a binomial experiment.
• What is a success in this experiment?
• A success is when a patient recovers fully.
• Specify the value of \(n\)
• The number of trials (patients) \(n = 5\)
• Specify the value of \(p\)
• The probability of success (patient recovers fully) \(p = 0.5\)
• Specify the value of \(q\)
• Since \(q=1 - p\), then \(q = 1-0.5=0.5\)
• List the possible values of the random variable \(x\)
• The random variable \(x\) represents the number of patients that recover fully. Since there are \(5\) patients, \(x = 0,1,2,3,4,5\)

Answer:

• Is the experiment a binomial experiment? Yes
• What is a success in this experiment? A patient recovers fully
• Specify the value of \(n\): \(n = 5\)
• Specify the value of \(p\): \(p = 0.5\)
• Specify the value of \(q\): \(q = 0.5\)
• List the possible values of the random variable \(x\): \(x = 0,1,2,3,4,5\)