48 A hospital is concerned about the risk of patients contracting an infection after a one-week or longer stay in the hospital. A long-term study estimates that the chance of contracting an infection after a one-week or longer stay in a hospital is 10%. A random sample of 50 patients who have been in the hospital at least 1 week is selected.

a. If the 10% infection rate is correct, what is the probability that at least 5 patients out of the 50 will have an infection?

b. What assumptions are you making in computing the probability in part (a)?

A box contains 10 light bulbs of which 3 are defective and 7 are not. An inspector randomly samples 3 bulbs without replacement Let X= the number of defective bulbs selected 

a. Construct the probability distribution of a.

b. What is the probability that at least one defective is selected?

c. What is the probability that the sample will contain at least one good buib?

According to a report from the District Health Secretariat of Barranquilla, the patients who suffer from measles, if they are cared for in a health center, the 2/5 are cured after 20 days. Understanding that the cure of one person is an independent event of the cure of another, of three patients who are currently in the health center, calculate:

a) The probability of being cured at least 1
b) The probability that at least 2 are cured

 A psychology class consists of 14 males and 36 females. If the professor selects names from the class using random sampling, a. What is the probability that the first student selected will be a female? b. If a random sample of n=3 is selected and the first two are both females, what is the probability that the third student selected will be a male? c. If a random sample of n=3 is selected and the first two are both females, what is the probability that the third student selected will be male if the professor samples with replacement?