# Example Of A Binomial Experiment

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Example 3 A box contains 20 cell phones, and two of them are defective. Three cell phones are randomly selected from this box and inspected to determine whether each of them is good or defective. Is this experiment a binomial experiment?

1. This example consists of three identical trials.

2. Each trial has two outcomes: good or defective.

3. The probability p is that a cell phone is good. The probability q is that a cell phone is defective. These two probabilities do not remain constant for each selection. They depend on what happened in the previous selection.

4. Because p and q do not remain constant for each selection, trials are not independent.

Given that the third and fourth conditions of a binomial experiment are not satisfied, this is not an example of a binomial experiment.

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For a binomial experiment, the probability of exactly x successes in n trials is given by the binomial formula

P( x ) n C x p x q n x where n = total number of trials p = probability of success q = 1 – p = probability of failure x = number of successes in n trials n - x = number of failures in n

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If at least four cameras of the given model are demanded the stock will run out. Consequently the probability that the cameras in stock will run out is

P(at least 4) = P(x≥ 4)=1- P(x -.8)

c) P (z > 1.64)

P(1.5 z 2.2) P( z 2.2) P( z 1.5)

.9861 .9332 .0529

=NORM.S.DIST(2.2;TRUE)-NORM.S.DIST(1.5;TRUE)

P( z .8) 1 P( z .8) 1 .2119 .7881

=1-NORM.S.DIST(-0.8;TRUE)

P( z 1.64) 1 P( z 1.64) 1 .9495 .0505

=1-NORM.S.DIST(1.64;TRUE)

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Converting an x Value to a z Value

For a normal random variable x, a particular value of x can be converted to its corresponding z value by using the formula

z

x

where μ and σ are the mean and standard deviation of the normal distribution of x, respectively.

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Example Let x be a continuous random variable that has a normal distribution with a mean of 60 and a standard deviation of 10. Find the area under the normal distribution curve

a) from x = 80 to x = 90

b) to the left of 40

80 60

2

10

90 60

For x = 90: z