A school board is considering implementing a new literacy program to help improv

Question

A school board is considering implementing a new literacy program to help improve their students’ literacy skills. As a first step, they wish to find out how their students’ literacy skills compare to provincial standards. So, they administer a literacy test with all their Grades 3-6 students and discover that the scores have mean 105 and standard deviation 15. The minimum provincial standard for this literacy skills test for Grades 3-6 students is 90.

a. We are interested in the percentage of classes in the school district that do not meet this provincial standard, on average. Assume all classes contain 30 children and it is reasonable to think of classes as simple random 3 samples of Grades 3-6 children from the school district. If there is enough information given in this question to compute this percentage, compute it and show your steps. If not, explain why not.

b. We are interested in the percentage of students in the district that do not meet the provincial standard. If there is enough information given in this question to compute this percentage, compute it and show your steps. If not, explain why not.

Explanation / Answer

Students mean literacy test score is 105 with standard deviation of 15.

a.

Given, classes as simple random 3 samples of Grades 3-6 children. So, the mean score of classes will be 105 with standard error = 15 / sqrt(3) = 8.66

So, the percentage of classes in the school district that do not meet this provincial standard = probability that the mean test score of class is less than 90 = P(X < 90)

= P[Z < (90 - 105) / 8.66 ] = P(Z < -1.732) = 0.0416

Thus, 4.16% of classes in the school district do not meet the provincial standard, on average.

b.

The percentage of students in the school district that do not meet this provincial standard = probability that the mean test score of students is less than 90 = P(X < 90)

Assuming the literacy test score follows a normal distribution,

P(X < 90) = P[Z < (90 - 105) / 15 ] = P(Z < -1) = 0.1587

Thus, 15.87% of students in the school district do not meet the provincial standard, on average.

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