The australain sheep dog is breed renowned for its intelligence and work ethic it is estimate that 45% of adult australian sheep dogs weigth 65pounds or more asample of 15 adult dogs is studied what is the probalilty that more than 12 of them weigh 65 lb

The probability is 0.0011 to 4 d.p

Step-by-step explanation:

Let p = probability of the dog weighing more than 65 pounds or more = 45% = 45/100 = 0.45

q is weighing less than = 1-p = 1 - 0.45 = 0.55

So the probability of more than 12 weigh 65 lb

That means 13, 14 or 15 weigh more than 65 lb

We can use Bernoulli approximation of Binomial distribution to get this;

That would be ;

15 C 13 0.45^13 0.55^2 + 15 C 14 0.45^14 0.55 + 15 C 15 0.45^15 0.55^0

= 0.001107024147 Which is approximately 0.0011 to 4 decimal place

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.