1. A study found that 35% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twnety-five percent of the ART pregnancies resulted in multiple births.
a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth.
b) Find the probability that a random selected ART cycle that resulted in a pregnancy did not produce a multiple birth.
c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth?
(Round to the nearest thousandth.)
2. The amounts a soft drink machine is designed to disperse for each drink are normally distributed, with a mean of 11.7 fluid ounces and a standard 0f 0.3 fluid ounce. A drink is randomly selected.
a) Find the probability that the drink is less than 11.6 fluid ounces.
b) Find the probability that the drink is between 11.3 and 11.6 fluid ounces.
c) Find the probability that the drink is more than 12.2 fluid ounces.
(Round to four decimal places.)
3. In the general population, one woman in ten will develop breast cancer. Research has shown that 1 woman in 650 carries a mutation of the BRCA gene. Seven out of 10 women with this mutation develop breast cancer.
Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene. (Round to one decimal place.)