# statistics

posted by jimmy

The Better Businesss Bureau reports that they resolve 70% of the consumer complaints they receive.
a) if a random sample of 5 consumer complaints is selected, what is the probability that all 5 were resolved?
b)if a random sample of 5 consumer complaints is selected, what is the probability that at least 1 was not resolved?
c) if a random sample of 5 consumer complaints is selected, what is the probability that none were resolved?
d) if a random sample of 5 consumer complaints is selected, what is the probability that at least 1 was resolved?

1. MathMate

Use binomial theorem with N=5, p=0.70
=> q=1-p=0.3
Let
C(n,r)=binomial coefficient=n!/(r!(n-r)!)

(a) all five resolved
P(X=5)=C(5,5)p^5q^0=1*0.7^5*1=0.17

(b) at least one not resolved
i.e. not all five
P(X≤4)=1-P(X=5)

(c) none resolved
P(X=0)=C(5,0)p^0q^5=1*1*0.3^5=0.002

(d) at least one resolved
i.e. not none resolved
P(X≥1)=1-P(X=0)

2. MathMate

A little suggest for follow-ups to my responses.
Start with a follow-up to the original post. If your patience runs out, then start a new post with or without the recipient's name under "school subject".

Assuming you have no problem with parts (a) and (c), parts (b) and (d) are simply the complement to the preceding part.

For example,
P(X≤4) means P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4).

However, we make use of the fact that the sum of probabilities of all possible events add up to 1, or

P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=1 (all possible events), so by transposition, we obtain:

P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
=1-P(X=5)
as was done in (b) and (d).

## Similar Questions

The number of complaints received by a business bureau can be represented by the following probability distribution. Find the expected number of complaints per day. complaints per day -0,1,2,3,4,5 probability-0.01,0.11,0.26,0.28,0.19,0.12 …
2. ### Statistics

he Oil Price Information Center reports the mean price per gallon of regular gasoline is \$ 3.79 with a population standard deviation of \$ 0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular …
3. ### Statistics

A consumer protection group reports that 25% of 5-lb bags of sugar of a certain brand are underweight. Three bags of sugar are selected at random. Assume that the report is correct. a. What is the probability that all three bags are …
4. ### statistics

random sample of n = 16 scores is selected from a normal distribution with a mean of μ = 50 and standard deviation of σ = 10. a. what is the probability that the sample mean will have a value between 45 and 55?
5. ### statistics

A specific study found that the average number of doctor visits per year for people over 55 is 8 with a standard deviation of 2. Assume that the variable is normally distributed. 1. Identify the population mean. 2. Identify the population …
6. ### algebra 1

Circle the most appropriate description. 27.A city planning commitee surveys 100 people waiting at a bus stop about the expansion of the public transportation system. Random Sample,systematic sample,self-selected sample, convenience …
7. ### Algebra 1

Can you please check my work? A city planning committee surveys 100 people waiting at a bus stop about the expansion of the public transportation system. Is this an example of a: random sample, systematic sample, self-selected sample,
8. ### Personal Finance

Most consumer complaints are resolved by: A. legal action. B. assistance from a government agency. C. contacting a company's headquarters. D. returning to the place of purchase. I believe it's C
9. ### Statistics

The ratio of brown M&M’s in a bag is stated by the candy company to be 56%. If a random sample of 500 bags is selected, determine the probability that the sample proportion of random bags of M&M’s selected has a percentage of brown …
10. ### Algebra 1

A city planning committee surveys 100 people waiting at a bus stop about the expansion of the public transportation system. Is this an example of a: random sample, systematic sample, self-selected sample, convenience sample, bipartisan …

More Similar Questions