Name:______
AP Stats/ ______
Date: ______Date Due:______
AP Statistics
6.3 Homework Worksheet
Binomial and Geometric Random Variables
Please show all work on a separate piece of paper
For numbers 1-4 explain whether the given random variable has a binomial distribution:
1)Seed Depot advertises that 85% of its flower seeds will germinate (grow). Suppose that the company’s claim is true. Judy buys a packet with 20 flower seeds from Seed Depot and plants them in her garden. Let X= the number of seeds that germinate.
2)Put the names of all the students in your class in a hat. Mix them up, and draw four names without looking. Let Y = the number whose last names have more than six letters.
3)Exactly 10% of the students in a school are left handed. Select students at random from the school, one at a time, until you find one who is left handed. Let V= the number of students chosen.
4)Exactly 10% of the students in a school are left handed. Select 15 students at random from the school, one at a time, and define W= the number who are left handed.
5)When an opinion poll calls residential telephone numbers at random, only 20% of the calls reach a live person. You watch the random digit dialing machine make 15 calls. Let X= the number of calls that reach a live person.
- Find and interpret
- Find and interpret
6)A federal report finds that lie detector tests given to truthful persons have probability about 0.2 of suggesting that the person is deceptive.A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X = the number of people who the lie detector says are being deceptive.
(a) Find and interpret μX.
(b) Find and interpret σX.
7)Major universities claim that 72% of their senior athletes graduate that year. Fifty senior athletic students attending major universities are randomly selected and recorded in order of selection.
- What is the probability that exactly 40 senior athletic students graduate that year?
- What is the probability that 40 or 41 or 42 senior athletic students graduated that year?
- What is the probability that 40 or fewer senior athletic students graduated that year?
- What is the probability that 41 or more senior athletic students graduated that year?
- What is the probability that 40 or more senior athletic students graduated that year?
- What is the probability that the first senior athletic student to graduate in the group of 50 that year is the 5th selected?
- What is the probability that the first senior athletic student to graduate in the group of 50 that year is the 30th selected?
- What is the probability that the first senior athletic student to graduate in the group of 50 that year is within the first 2 selected?
Multiple Choice:
8)Joe reads that 1 out of 4 eggs contains salmonella bacteria. So he never uses more than 3 eggs in cooking. If eggs do or don’t contain salmonella independently of each other, the number of contaminated eggs when Joe uses 3 chosen at random has the following distribution:
(a) binomial; n = 4 and p = 1/4
(b) binomial; n = 3 and p = 1/4
(c) binomial; n = 3 and p = 1/3
(d) geometric; p = 1/4
(e) geometric; p = 1/3
9)In the previous exercise, the probability that at least 1 of Joe’s 3 eggs contains salmonella is about
(a) 0.84.
(b) 0.68.
(c) 0.58.
(d) 0.42.
(e) 0.30.