Question

Suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. You find an individual that reads 56.2 word per minute. You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 95 words per minute and a standard deviation of 22 words per minute.

a. At what percentile is the child's reading level (round final answer to one decimal place).

b. Create a graph with a normal curve that illustrates the problem.

For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the student's percentile. There is a Normal Distribution Graph generator linked in the resources area. Upload file containing your graph below.

c. Make an argument to the parents of the child for the need for remediation. Structure your essay as follows:

1. A basic explanation of the normal distribution
2. Why the normal distribution might apply to this situation
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. Interpret the answer to part a. including a definition of percentile.
5. Explain how the graph created in part b. represents the child's reading level.
6. Use the answers to parts a. and b. to emphasize the gravity of the situation.
7. Give a suggested course of action.

Answer 1

Answer to part a)
The specific normal distribution for this question is as follows:

Mean = 95

Mean - SD = 95-22 = 73

Mean -2*SD = 95-2*22 = 51

Mean + Sd = 95+22 = 117

Mean + 2*SD = 95+2*22 = 139

.

the students score is : x = 56.2

To find the percentile: first step is to find the Z value , and then we refer to the Z table to trace the percentile corresponding to the Z value obtained

Z = (x - M) / SD

Z = (56.2 -95)/22

Z = -1.76

.

Refer to the Z table:

.

The percentile of this score is : 0.0392 * 100 = 3.92 ~3 percentile

which is extremely low

A percentile value of less than 0.05 is considered to be UNUSUAL , hence this students reading score is exceptionally low

.

Part b)

.

Answer to part c)

Normal distribution: is the most common distribution , in which mean and standard deviation are the only two parameters of the population that are provided. it applies to the variables that are normally distributed. for example height of adults. There are very few people with extremely high or extremely low scores, but you would find many people in the average score range

Likewise the reading skill of the students is considered

you would find majority of the students who have average reading skill, but there would be very few would perform exceptionally well and very few students who would perform exceptionally low

This trend of the variable so follows in called the normal distribution

if the percentile of score is less than 0.05 , this implies that the reading ability of the child is extremely low than the usual and one needs to take special action to ensure that the reading ability of the child improves

The score is 56.2 words per minute as compared to the average score of 95 words per minute, with a standard deviation of 22 words per minute

The percentile of this score is 3.92% , that means the child reading ability comes under the lower 4% of the students, which is not good. and strong action needs to be taken to cause improvement in the reading speed of the child, so that the score improves comes in the range of usual scores to ensure normal brain growth of the child