Question

Walmart uses it records and determines that the average amount spent by a customer is 820

with a standard deviation of $15
ц = $20,
0 = $15.
Suppose 4 customers walk into 4 diferent Walmarts and spend amounts X1, X2, X3, and X4.
Then the variables are independent. Let 2 be the average of the four returns; that is,
X1 + X, + X3 + X
(a) Find uz.

(b) Find oz.

Answer 1

To find the z-score for the average amount spent by the four customers at different Walmarts, use the formula z = (X - μ) / σ. To find the probability, use the t-distribution and find the critical value (t-critical) for a given confidence level and degrees of freedom. Multiply the critical value by the standard deviation of the sample mean to calculate the margin of error.

Step-by-step explanation:

(a) To find the z-score, we can use the formula:

z = (X - μ) / σ

Where:

X is the value we want to find the z-score for (in this case, the average of the four returns)

μ is the population mean (given as 820)

σ is the population standard deviation (given as 15)

Since we have the population mean and standard deviation, we can directly calculate the z-score as follows:

z = (2 - 820) / 15

(b) To find the probability, we can use the standard normal distribution table. However, since we are dealing with a sample mean, we need to account for the sample size and use the t-distribution instead. We would need the degrees of freedom, which is one less than the sample size. In this case, it would be 3 (4 customers - 1). We can find the critical value (t-critical) for a given confidence level and degrees of freedom. Finally, we can calculate the margin of error by multiplying the critical value by the standard deviation of the sample mean (given as 15/sqrt(4)).