Question

The distribution of heights of both five‑year old boys and seven‑year old boys is approximately Normal. The mean height of a five‑year old boy is 43 inches and the standard deviation is 1.8 inches. The mean height of a seven‑year old boy is 48 inches and the standard deviation is 2.1 inches. John's height was 44 inches on his fifth birthday, and today, on his seventh birthday, he measures 49 inches tall. What can you conclude about the rate of John's growth when compared to other boys his age?

(a) Calculate John's standardized score, or -score, at age 5. (Enter your answer rounded to three decimal places.)

(b) Calculate John's standardized score at age 7. (Enter your answer rounded to three decimal places.)

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

5 years old:

Mean height (m) = 43

Standard deviation (σ) = 1.8

Height on fifth birthday (x) = 44

7 years old:

Mean height (m) = 48

Standard deviation (σ) = 2.1

Height on 7th birthday (x) = 49

To get the standardized score :

USe :

Zscore = (x - mean) / standard deviation

At 5 years:

Zscore = (44 - 43) / 1.8

Zscore = 1/ 1.8

Zscore = 0.556

At 7 years:

Zscore = (49 - 48) / 2.1

Zscore = 1/ 2.1

Zscore = 0.476

At the different ages, John's growth rate in height declined after the 5 th years as the standardized score at 5 years is greater than at 7 years.