The distribution of the diameters of a particular variety of grapes is approximately normal with a standard deviation of 0.3 cm.How does the diameter of a grape at the 67th percentile
Compare with the mean diameter?
A)0.201 cm below the mean
B)0.132 cm below the mean
C)0.132 cm above the mean
D)0.201 cm above the mean

Question

Quizplus · Accepted Answer

The 67th percentile in a normal distribution is above the mean. Using the Z-table, a percentile of 67 corresponds to a Z-score of approximately 0.44. Multiplying the Z-score by the standard deviation (0.44 * 0.3 cm) gives approximately 0.132 cm, indicating that the diameter at the 67th percentile is 0.132 cm above the mean.

The Distribution of the Diameters of a Particular Variety of Grapes