According to the pew research center, approximately 60% of U.S. adults have researched health information.

a. if a sample of 13 U.S. adults is selected, calculate the probability that at least 11 have researched health info.

b. Calculate the mean and variance of the number of U.S. adults who have searched online for health info. for a sample size of 90.

Question

According to the pew research center, approximately 60% of U.S. adults have researched health information.

a. if a sample of 13 U.S. adults is selected, calculate the probability that at least 11 have researched health info.

b. Calculate the mean and variance of the number of U.S. adults who have searched online for health info. for a sample size of 90.

kropot72 · Answer

a. The probability that a randomly selected adult has researched health information is 0.6. The required probability can be found by finding the probability that 12 or 13 have researched health info and subtracting this from 1. Using the binomial distribution:
$$P(12)=13C12\times(0.6)^{12}\times0.4=13\times0.0021768\times0.4=you\ can\ calculate$$
$$P(13)=(0.6)^{13}=0.001306$$
The probability that at least 11 have researched health info is given by:
1.0000 - {P(12) + P(13)}=you can\ calculate