Respuesta :
Answer:
95% of the text messages have length between 23 units and 47 units.
Step-by-step explanation:
We are given the following in the question:
The lengths of text messages are normally distributed.
95% confidence interval:
(23,47)
Thus, we could interpret the confidence interval as:
About 95% of the text messages have length between 23 units and 47 units.
By Empirical rule for a normally distributed data, about 95% of data lies within 2 standard deviations of mean , thus we can write:
[tex]\mu - 2\sigma = 23\\\mu +2\sigma = 47\\\Rightarrow \mu = 35\\\Rightarrow \sigma = 6[/tex]
Thus, the mean length of text messages is 23 units and standard deviation is 6 units.
Answer:
Correct interpretation is provided below.
Step-by-step explanation:
We are given that the lengths of text messages are normally distributed with an unknown population mean.
Also, a random sample of text messages is taken and results in a 95% confidence interval of (23,47) characters.
Now, the correct interpretation of the 95% confidence interval is that we are 95% confident that the population mean will lie between the 23 and 47 as the confidence interval is estimated taking into consideration the population mean only.
