Answer:
The probability content for the confidence interval (3.49, 3.69) is 96%.
Step-by-step explanation:
The sample selected to determine the mean number of times the pet owners visited their veterinarian each year is of size, <em>n</em> = 475.
The sample selected is quite large, i.e. <em>n</em> > 30.
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we take appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
; for <em>n</em> → ∞.
And the standard deviation of the distribution of sample means is given by,
; for <em>n</em> → ∞.
So, the random variable <em>X</em>, defined as the number of visits to the veterinarian each year, follows a Normal distribution.
The (1 - <em>α</em>)% confidence interval for the population mean (<em>μ</em>) is:
The information provided is:
The confidence interval is (3.49, 3.69).
The margin of error of the confidence interval for the population mean is:
Compute the MOE as follows:
Compute the critical value of <em>z</em> as follows:
Compute the value of as follows:
Thus, the probability content for the confidence interval (3.49, 3.69) is 96%.