Answer:
Option a) circle 5 meters and 22 meters
Step-by-step explanation:
We are given the following information in the question:
A pair of diameter and the circumference is given. We have to find a correct approximations for the diameter and circumference.
a) circle 5 meters and 22 meters
b) 19 inches and 50 inches
c) 33 centimeters and 80 centimeters
Thus, no pair gives a reasonable approximation. Only the circle with diameter 5 and circumference 22 meters have closest approximation.
This question is incomplete, the complete question is;
Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and preview ads before the movie starts. Many complain that the time devoted to previews is too long (The Wall Street Journal, October 12, 2012). A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number,
a) If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, what sample size should be used? Assume 95% confidence.
b) If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.
Answer:
a) the required Sample Size is 40
b) the required Sample Size is 62
Step-by-step explanation:
Given the data in the question;
standard deviation σ = 4 minutes
a)
margin of error E = 75 seconds = ( 75 / 60 )minutes = 1.25 minutes
And 95% confidence.
Now, Critical Value of z for 0.95 confidence interval;
∝ = 1 - 0.95 = 0.05
= 1.96
so, sample size n will be;
n = [ × σ/E ]²
we substitute;
n = [ 1.96 × (4/1.25) ]²
n = [ 1.96 × 3.2 ]²
n = [ 6.272 ]²
n = 39.338
Since we referring to a number of sample, its approximately becomes 40
Therefore, the required Sample Size is 40
b)
margin of error E = 1 minutes
And 95% confidence.
Now, Critical Value of z for 0.95 confidence interval;
∝ = 1 - 0.95 = 0.05
= 1.96
so, sample size n will be;
n = [ × σ/E ]²
we substitute;
n = [ 1.96 × (4/1) ]²
n = [ 1.96 × 4 ]²
n = [ 7.84 ]²
n = 61.466
Since we referring to a number of sample, its approximately becomes 62
Therefore, the required Sample Size is 62