The probability of obtaining a defective 10-year old widget is 73.2%. For our purposes, the random variable will be the number of items that must be tested before finding the first defective 10-year old widget. Thus, this procedure yields a geometric distribution. Use some form of technology like Excel or StatDisk to find the probability distribution.
(Report answers accurate to 4 decimal places.)
k P(X = k)
1 Correct
2
3
4
5
6 or greater

P(X=0)=0.732

P(X=1)=0.1962

P(X=2)=0.0526

P(X=3)=0.0141

P(X=4)=0.0038

P(X=5)=0.001 0

P(X≥6)=0.0004

Step-by-step explanation:

We want to find the probability distribution of X, where X is the number of items that must be tested before finding the first defective 10-year old widget.

This means that if X=2, the first two items are not defective and the third item is defective.

The probability of finding a defective item is p=0.732 for each trial.

Then, the probability for X=k can be written as:

Then, we can write:

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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