A recent survey found that 30% of telephone users have switched completely to cell phone use (i. e. they do not have landlines in their homes). A random sample of 10 of these customers is selected. What is the probability that exactly 30% of these 10 telephone users do not have landlines in their homes

The probability that exactly 30% of these 10 telephone users do not have landlines in their homes is 0.2668.

Step-by-step explanation:

We are given that a recent survey found that 30% of telephone users have switched completely to cell phone use (i.e. they do not have landlines in their homes).

A random sample of 10 of these customers is selected.

The above situation can be represented through binomial distribution;

where, n = number of trials (samples) taken = 10 customers

            r = number of success = 30% of 10 = 3

            p = probability of success which in our question is the probability

                  that telephone users do not have landlines in their homes,

                   i.e. p = 30%

Let X = Number of telephone users who do not have landlines in their homes

So, X ~ Binom(n = 10, p = 0.30)

Now, the probability that exactly 30% of these 10 telephone users do not have landlines in their homes is given by = P(X = 3)

           P(X = 3) =  

                         =  

                         =  0.2668

b

step-by-step explanation:

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.