An advertising agency that serves a major radio station wants to estimate the mean amount of time the station’s audience members listen to the radio on a daily basis. From past studies the population standard deviation is known to equal 45 minutes. What sample size is needed if the agency wants to be 90% confident of being within (±) 5 minutes of the true mean amount of time audience members listen to the radio per day?

So the answer for this case would be n=220 rounded up to the nearest integer

Step-by-step explanation:

Information given

represent the population deviation

represent the margin of error

The margin of error for the true mean is given by this formula:

   (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (4) we got:

  (b)

The critical value for 90% of confidence interval now can be founded using the normal distribution. The significance level is and the critical value would be , replacing into formula (b) we got:

So the answer for this case would be n=220 rounded up to the nearest integer

60.96438

step-by-step explanation:

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.