Question

Suppose that the population mean waist size is 85cm and that the population standard deviation is 15cm.

a. Calculate the z-score for a waist size of 90cm.
b. Determine the range of waist sizes in the population.
c. Identify the mode of the waist size distribution.
d. Assess the skewness of the waist size data.

Answer 1

a. The z-score for a waist size of 90cm is 1.

b. The range of waist sizes in the population cannot be determined with the information provided.

c. The mode of the waist size distribution cannot be determined with the information provided.

d. The skewness of the waist size data cannot be determined with the information provided.

Step-by-step explanation:

a. To calculate the z-score, you use the formula:
`\( Z = ((X - \mu))/(\sigma) \), where \( X \) is the value, \( \mu \) is the mean, and \( \sigma \)`is the standard deviation. In this case,
`\( Z = ((90 - 85))/(15) = 1 \).`

b. The range is the difference between the maximum and minimum values in a dataset. However, the information provided only includes the mean and standard deviation, not individual data points, so the range cannot be determined.

c. The mode is the value that appears most frequently in a dataset. Without specific data points, the mode cannot be determined.

d. Skewness measures the asymmetry of a distribution. To assess skewness, you need the actual dataset. Without this information, skewness cannot be determined. The mean and standard deviation alone do not provide insight into the shape of the distribution.