Question

A common concern of parents is the language development of their child. In some cases, a language deficit is an isolated problem; however, in other cases the language deficit could be a symptom of a cognitive deficit such as autism. Say a parent brings 5-yr-old john for an assessment, and john is given a Language test and a seperate Intelligence test. His test score on the Language test reveals 96 correct answers. His test score on the seperate Intelligence test reveals 61 correct answers. The data available for johns age group from all school districts in the city shows that the number of correct Intelligence test answers of children his age is normally distributed with a mean of 50 and a standard deviation of 5. The number of correct Language test answers of children his age is normally distributed with a mean of 103 and a standard deviation of 3. Show all work.

A) Calculate Johns Z scores (using the Z score formula)for the intelligence and language tests.

B) Based on the Z scores, how does john compare to his peers in terms of his language? intelligence?

C) Using the normal curve table, which percentage of children score above and below johns language score?

D) Using the normal curve table, which percentage of children score above and below Johns intelligence score?

E) What advice would you give jogns parents and why?

Answer #1

**Solution:-**

μ_{Language} = 103, σ_{Language} = 3

μ_{Intelligence} = 50, σ_{Intelligence} = 5

**A) Johns Z scores for the intelligence and language
tests is - 2.33 and 2.2.**

x_{Language} = 96

By applying normal distribution:-

z = - 2.333

x_{Intellignece} = 61

By applying normal distribution:-

z = 2.2

**B) He performed really well in Intelligence test as
compared to his friends.**

**He performed really bad in Language test as compared to
his friends.**

**C) The percentage of children score above and below
johns language score is 99.01% and 0.99%.**

**P(z > - 2.33) = 99.01%'**

**P(z < - 2.33) = 0.99%**

**D) The percentage of children score above and below
Johns intelligence score is 1.39% and 98.61%.**

**P(z > 2.2) = 1.39%**

**p(z < 2.2) = 98.61%**

**E) John should work hard on Language as his score is
very low as compared to his class.**

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