In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 54.4 inches, and standard deviation of 7.9 inches.

A) What is the probability that a randomly chosen child has a height of less than 46.35 inches?

Answer=

(Round your answer to 3 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 38.6 inches?

Answer=

Given Information:  

Mean height of ten year children = μ =  54.4 inches

Standard deviation = σ = 7.9 inches

Required Information:  

A) What is the probability that a randomly chosen child has a height of less than 46.35 inches?

B) What is the probability that a randomly chosen child has a height of more than 38.6 inches?

Explanation:

Let X is the random variable that represents height measurements of ten-year-old children with mean of 54.4 inches and standard deviation of 7.9 inches.

A) The probability that a randomly chosen child has a height of less than 46.35 inches is given by

From the z-table , the z-score corresponding to -1.02 is 0.1538  

Therefore, 15.38% children has a height of less than 46.35 inches.

B) The probability that a randomly chosen child has a height of more than 38.6 inches is given by

From the z-table , the z-score corresponding to -2 is 0.0227

Therefore, 97.73% children has a height of greater than 38.6 inches.

is only a line? i think so

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."