Question

1. - / 5 points about 65% of babies born with a certain ailment recover fully. a hospital is caring for 8 babies born with this ailment. the random variable represents the number of babies that recover fully. decide whether the experiment is a binomial experiment. if it is, identify a success, specify the values of n and p, and list all the possible values of the random variable, x. (a) is the experiment a binomial experiment? yes no (b) what is a success in this experiment? this is not binomial. the baby does not recover fully. the baby recovers fully. (c) specify the value of n. this is not binomial. n=5.2 n=8 n=65 (d) specify the value of p. p=8 p=65 p=0.65 this is not binomial. (e) list the possible values of the random variable. x = 1, 2, ..., 7 x = 0, 1, 2, ..., 7 x = 0, 1, 2, ..., 8 x = 1, 2, ..., 8 this is not binomial. 4. - / 7 points

Explanation:

Part (a)

A binomial experiment has 4 conditions: fixed number of trials, independent trials, two outcomes (success/failure), and constant probability of success. Here, 8 babies (fixed trials), each recovery is independent, two outcomes (recover or not), and probability of recovery (success) is 0.65 (constant). So it is a binomial experiment.

In this context, "success" is defined as the event we're interested in, which is a baby recovering fully (since we're measuring the number of babies that recover fully).

In a binomial experiment, \( n \) is the number of trials. Here, there are 8 babies (trials), so \( n = 8 \).

Answer:

Yes

Part (b)