Question

The spending at Target is distributed normally with a mean spending of $47.67 and a standard deviation of $5.50. What is the probability that the spending is between 46 and 49.56 dollars?

Answer 1

Answer 2

To calculate the probability that the spending at Target is between $46 and $49.56, we need to standardize the values and then use the standard normal distribution table or a statistical calculator.

First, we calculate the z-scores for the given values using the formula:

z = (x - mean) / standard deviation

For $46: z1 = (46 - 47.67) / 5.50 = -0.3036

For $49.56: z2 = (49.56 - 47.67) / 5.50 = 0.3436

Next, we use the standard normal distribution table or a statistical calculator to find the area under the curve between these two z-scores. The area represents the probability.

Using the standard normal distribution table, we find the following probabilities:

Area to the left of z1 = 0.3809 Area to the left of z2 = 0.6331

To find the probability between the two values, we subtract the area to the left of z1 from the area to the left of z2:

Probability = Area to the left of z2 - Area to the left of z1 Probability = 0.6331 - 0.3809 Probability = 0.2522

Therefore, the probability that the spending at Target is between $46 and $49.56 is approximately 0.2522, or 25.22%