Question

the test scores for the verbal reasoning and the quantitive reasoning section of the graduate record examination are normally dostributed. in a recent year, the mean test score was 150 and the standard deviation was 8.75. the test score of a student is selected at random. what is the probability of the students test score between 143 and 162? round your answer to 4 decimals.

Answer 1

Solution :

Let X be a random variable which represents the test scores for the verbal reasoning and the quantitive reasoning section of the graduate record examination.

Given that,  

μ = 150 and σ = 8.75

We have to obtain that P(143 < X < 162).

We know that, if X ~ N(μ, σ²) then,

Using "pnorm" function of R we get,

P(Z < 1.3714) = 0.9149 and P(Z < -0.8) = 0.2119

Hence, the probability of the student's test score between 143 and 162 is 0.7030.

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