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.)

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.

529 and 531

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.