Question

explain the meaning of the following percentiles in parts (a) and (b). (a) the 5th percentile of the weight of males 36 months of age in a certain city is 11.0 kg. (b) the 95th percentile of the length of newborn females in a certain city is 53.3 cm. (a) choose the correct answer below. a. 5% of males weigh 11.0 kg or less, and 95% of 36 - month - old males weigh more than 11.0 kg. b. 5% of 36 - month - old males weigh 11.0 kg or less, and 95% of 36 - month - old males weigh more than 11.0 kg. c. 5% of males weigh 11.0 kg or more, and 95% of 36 - month - old males weigh less than 11.0 kg. d. 5% of 36 - month - old males weigh 11.0 kg or more, and 95% of 36 - month - old males weigh less than 11.0 kg. (b) choose the correct answer below. a. 95% of females have a length of 53.3 cm or less, and 5% of newborn females have a length that is more than 53.3 cm. b. 95% of females have a length of 53.3 cm or more, and 5% of newborn females have a length that is less than 53.3 cm. c. 95% of newborn females have a length of 53.3 cm or more, and 5% of newborn females have a length that is less than 53.3 cm. d. 95% of newborn females have a length of 53.3 cm or less, and 5% of newborn females have a length that is more than 53.3 cm.

Explanation:

The pth percentile of a data set is the value such that p percent of the data values are less than or equal to that value. For the 5th percentile, 5% of the data values are less than or equal to it and 95% are greater. For the 95th percentile, 95% of the data values are less than or equal to it and 5% are greater.
For part (a), we are considering the 5th percentile of the weight of 36 - month - old males. So 5% of 36 - month - old males weigh 11.0 kg or less and 95% weigh more.
For part (b), we are considering the 95th percentile of the length of newborn females. So 95% of newborn females have a length of 53.3 cm or less and 5% have a length that is more.

Answer:

(a) B. 5% of 36 - month - old males weigh 11.0 kg or less, and 95% of 36 - month - old males weigh more than 11.0 kg
(b) D. 95% of newborn females have a length of 53.3 cm or less, and 5% of newborn females have a length that is more than 53.3 cm