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In: Statistics and Probability

(4 pts) The Graduate Record Examination (GRE) is a test required for admission to many U.S....

(4 pts) The Graduate Record Examination (GRE) is a test required for admission to many U.S. graduate schools. Students' scores on the quantitative portion of the GRE follow a normal distribution with mean 150 and standard deviation 8.8. In addition to other qualifications, a score of at least 160 is required for admission to a particular graduate school.

Suppose n = 16 randomly selected students take the GRE on the same day.

  1. Describe the sampling distribution of the sample mean for the quantitative GRE Scores for the 16 students. (give the shape, mean, and SD)
  1. What is the probability that a random sample of 16 students has a mean score on the quantitative portion of the GRE that is less than 147? Would this be an unusual outcome.

Solutions

Expert Solution

Solution :

Given that ,

mean = = 150

standard deviation = = 8.8

n = 16

Shape is approximately normal .

= 150 and

= / n = 8.8 / 16 = 8.8 / 4 = 2.2

P( < 147) = P(( - ) / < (147 - 150) / 2.2)

= P(z < -1.36)

Using standard normal table,

= 0.0869

Probability = 0.0869

Probability > 0.05

Outcome is not unusual .

orchestra answered 3 years ago
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