SOLUTION: An AP Statistics teacher is desperately rummaging around her box of AAA batteries trying to find 2 working batteries for a student’s graphing calculator. The teacher has 10 batt

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Question 1178477: An AP Statistics teacher is desperately rummaging around her box of AAA batteries trying to find 2 working batteries for a student’s graphing calculator. The teacher has 10 batteries, 3 of which are dead. The teacher randomly selects two batteries.

Create a probability model (values for a random variable and corresponding probabilities) for the number of good batteries (4 points):

What is the expected number of good batteries the teacher selects? (3 points):

What is the standard deviation? (3 points):


Found 2 solutions by ewatrrr, Boreal:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
The teacher has 10 batteries, 3 of which are dead.
10 Batteries: 7G and 3B
The teacher randomly selects two batteries.

Create a probability model:
P(x=0) + P(x=1) + P(x=2) = 1

What is the expected number of good batteries the teacher selects?
 0(3C2)(7C0)/(10C2) + 1(7C1)(3C1)/(10C2) + 2(7C2)(3C0)/(10C2) 
  21/45 + 42/45 = 63/45 = 1.4

Wish You the Best in your Studies.


Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
p(0 good) is (3/10)(2/9)=1/15
this is also 3C2*7C0/10C2=3/45=1/15
-
p(1) is 3C1/7C1/10C2=21/45 or 7/15
or (3/10)*(7/9)+(7/10)*(3/9)=42/90=7/15
-
p(2)=(7/10)(6/9)=42/90 or21/45=7/15
3C0*7C2/10C2=21/45=7/15
-
the probabilities add up to 1.
-
Expected value is 0*(1/15)+1(7/15)+2(7/15)=21/15, or 1.4 batteries
-
variance is sum of squared deviations or (-1.4)^2*0+(-0.4)^2*(7/15)+(0.6)^2*(7/15)
=0+0.074666+0.168
sd is sqrt (0.24266)=0.493
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