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September 20, 2014

September 20, 2014

Posted by **Sarah** on Thursday, August 30, 2012 at 10:33pm.

a. all 25 returns are free of arithmetic errors.

b. at most 23 returns are free of arithmetic errors.

c. more than 17 are free of arithmetic errors

- statistics -
**MathMate**, Friday, August 31, 2012 at 7:21amThis problem has the following characteristics:

1. Number of trials is fixed (25) and known.

2. The probability of success is constant (0.9) throughout the trials and known.

3. The tests are independent

4. Each test is Bernoulli (i.e. true/false, 0/1)

These criteria indicate the binomial distribution, with

n=25, p=0.9, q=(1-0.9)=0.1

with

P(X=k)=C(n,k)p^{k}q^{n-k}

a.

Calculate P(X=25)

b.

calculate p=P(X=24)+P(X=25)

Probability for at most 23

=1-(P(X=24)+P(X=25))

c.

calculate

25

∑ P(X=k)

k=18

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