11. Suppose that a family has 7 children. Also, suppose that the probability of having a girl (based on the gender assigned at birth) is 1/2. Find the probability that the family has at least 6 girls.

The probability that the family has at least 6 girls is _______.

(integer or a simplified fraction.)

12. A survey finds that customers are overcharged by price scanning systems, on average, on 1.70% of items. Suppose a customer purchases 16 items. Find the following probability. A customer is not overcharged for any item.

The probability is________. (Round to four decimal places as needed.)

13. A recent study found that 82% of breast-cancer cases are detectable by mammogram. Suppose a random sample of 14 women with breast cancer are given mammograms. Find the probability that all of the cases are detectable, assuming that detection in the cases is independent.

The probability that all of the cases of breast cancer are detectable is about

_______. (Round to four decimal places as needed.)

14. A recent survey found that 87% of first-year college students were involved in volunteer work at least occasionally. Suppose a random sample of 14 college students is taken. Find the probability that at least 11 students volunteered at least occasionally.

The probability that at least 11 students volunteered at least occasionally is______. (Round to four decimal places as needed.)

15. For the experiment described below, let x determine a random variable, and use your knowledge of probability to made a probability distribution. Threecardsaredrawn(withreplacement)and the number of redcards is noted.

Number of complaints per day 0 2 3 4 5 6 0 Probability 0.02 0.06 0.13 0.24 0.35 0.1 0.1 Find the expected number of complaints per day