A marketing research assistant for a veterinary hospital surveyed a random sample of 457 pet owners. Respondents were asked to indicate the number of times that they visit their veterinarian each year. e sample mean response was 3.59 and the sample standard deviation was 1.045. Based on these results, a condence interval from 3.49 to 3.69 was calculated for the population mean. Find the probability content for this interval

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, n = 475.

The sample selected is quite large, i.e. n > 30.

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 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 n → ∞.

And the standard deviation of the distribution of sample means is given by,

; for n → ∞.

So, the random variable X, defined as the number of visits to the veterinarian each year, follows a Normal distribution.

The (1 - α)% confidence interval for the population mean (μ) 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 z as follows:

Compute the value of as follows:

Thus, the probability content for the confidence interval (3.49, 3.69) is 96%.

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.