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```AP Statistics
6.3A Assignment
1. Explain whether the given random variable has a binomial distribution.
A. 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.
B – germinates or not
I – each seed is independent of the others
N – there are 20 trials
S – the probability of success is 0.85 for each seed
It is a binomial distribution
B. 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.
B – the student’s last name has 6 or more letters or not
I – the number of letters in each student’s last name is independent of the other student’s last name
N – there are 4 trials
S – the probability of success is not the same for each trial
It is not a binomial distribution
C. 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.
B – the student is left handed or not
I – whether or not a student is left handed is independent of the other student’s left handedness
N – there is not a set number of trials
It is not a binomial distribution
2. Suppose you purchase a bundle of 10 bare-root rhubarb plants. The sales clerk tells you that on average
you can expect 5% of the plants to die before producing any rhubarb. Assume that the bundle is a random
sample of plants. Let Y = the number of plants that die before producing any rhubarb.
A. Use the binomial probability formula to find P(Y = 1). Interpret this result in context.
 10 
1
9
P Y  1     0.05   0.95   0.3151
1 
B. Would you be surprised if 3 or more of the plants in the bundle die before producing any rhubarb:
P Y  3   1  P Y  2   1   P Y  2   P Y  1  P Y  0   
  10 
 10 
 10 
2
8
1
9
0
10 
 1      0.05   0.95      0.05   0.95      0.05   0.95    0.0115
1 
0 
2 

I would be surprised because the probability that 3 or more plants in the bundle would die by chance is
3. 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.
A. Find the probability that exactly 17 seeds germinate. Show your work.
 20 
17
3
P  X  17      0.85   0.15   0.2428
 17 
B. If only 12 seeds actually germinate, should Judy be suspicious that the company’s claim is not true?
Compute P(X < 12) and use this result to support your answer.
P  X  12   P  X  12   P  X  11  ...  P  X  0  
 20 
 20 
 20 
12
8
11
9
0
20
    0.85   0.15      0.85   0.15   ...     0.85  0.15   0.0059
 12 
 11 
0 
I would be surprised because the probability that 12 or less of the seeds would germinate by chance is