Respuesta :
Answer: A. The sampling follows a normal distribution.
B. Between 25.14 and 30.86
C. About 95% will contain the true mean and about 5% won't
Step-by-step explanation: A. The sampling is normally distributed because:
- it has a symmetric bell shape,
- mean and median are both the same and located at the center of graphic,
- approximately 68% of the data falls within one standard deviation;
- 95% falls within two standard deviations;
- 99.7% within 3 standard deviations;
B. For a 95% confidence interval: α/2 = 0.025
Since n = 210, use z-score = 1.96
To calculate the interval:
mean ± [tex]z.\frac{s}{\sqrt{n} }[/tex]
Replacing for the values given:
28 ± [tex]1.96.\frac{21}{\sqrt{210} }[/tex]
28 ± [tex]1.96*1.45[/tex]
28 ± 2.84
lower limit: 28 - 2.84 = 25.14
upper limit: 28 + 2.84 = 30.86
Confidence Interval is between 25.14 and 30.86.
C. Confidence Interval at a certain percentage is an interval of values that contains the true mean with a percentage of confidence. In the case of number of times per day students text, 95% of the interval will contain the true mean, while 5% will not contain it.
