Stats

tagiraldo · #1 $Old$ June 27th, 2009, 01:29 AM

Assume the market proportion of the phone provider XY to be 50% in a given country. Assume it means that 50% of all existing phone numbers in the country are of the provider XY.

a) What is the probability that from the 10 randomly selected phone numbers, the first two numbers are of the provider XY and the next 8 numbers are of some other provider?

b) What is the probability that 2 phone numbers out of 10 randomly selected are of the provider XY?

c) What is the probability that at least 2 phone numbers out of 10 randomly selected are of the provider XY?

d) If 100 numbers have been randomly selected, what is the probability that the we find at least 48 and less than 52 numbers that are of the provider XY?

CaptainBlack · #2 $Old$ June 27th, 2009, 01:54 AM

Quote:

Originally Posted by tagiraldo $View Post$

Assume the market proportion of the phone provider XY to be 50% in a given country. Assume it means that 50% of all existing phone numbers in the country are of the provider XY.

a) What is the probability that from the 10 randomly selected phone numbers, the first two numbers are of the provider XY and the next 8 numbers are of some other provider?

The probability that the first two numbers are from XY is $p_{XY}^2$ , the probability that the next 8 are from some other provider is $(1-p_{XY})^8$

The required probability is the product of these.

CB

CaptainBlack · #3 $Old$ June 27th, 2009, 02:02 AM

Quote:

Originally Posted by tagiraldo $View Post$

Assume the market proportion of the phone provider XY to be 50% in a given country. Assume it means that 50% of all existing phone numbers in the country are of the provider XY.

b) What is the probability that 2 phone numbers out of 10 randomly selected are of the provider XY?

c) What is the probability that at least 2 phone numbers out of 10 randomly selected are of the provider XY?

The number of XY's in a sample of size $N$ has a binomial distribution $B(p_{XY},N)$ . This will give the answer to b) straight off, for part c) you will need to sum the appropriate binomial probabilities.

Quote:

d) If 100 numbers have been randomly selected, what is the probability that the we find at least 48 and less than 52 numbers that are of the provider XY?

For this use the normal approximation to the binomial.

CB