A person picks a sample of 5 toothbrushes at random from a very large case of to

Question

A person picks a sample of 5 toothbrushes at random from a very large case of toothbrushes known to contain 10 percent defective toothbrushes. Construct a probability distribution for the number of defective toothbrushes, determine the expected value and the standard deviation of the distributution.

2) What is the probabilty that no more than two of the toothbrushes picked are defective?

3) Find the probability that at least four of the toothbrushes are defective

4) At most four four of the toothbrushes are defective.

Explanation / Answer

n = 5

p =0.1

a)

P(X =x) = 5Cx * 0.1^x * 0.9^5-x

mean = np = 5 * 0.1 = 0.5

standard deviation = sqrt(5 * 0.1 * 0.9) = 0.6708

2)

P(X <=2) = P(X=0) + P(X=1) + P(X=2)

= 5C0 * 0.9^5 + 5C1 *0.1 * 0.9^4 + 5C2 * 0.1^2 * 0.9^3

= 0.99144

3)

P(X>=4) = P(X=4) + P(X=5)

= 5C4 * 0.1^4 * 0.9 + 5C5 * 0.1^5

= 0.00046

4)

P(X<=4) = 1 - P(X=5)

= 1 - 0.1^5

= 0.99999

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