Graduate students applying for entrance to many universities must take a Miller

Question

Graduate students applying for entrance to many universities must take a Miller Analogies Test. It is known that the test scores have a mean of 75 and a variance of 16. In 1990, 100 students applied for entrance into graduate school in physics. (a)[3] Find the mean and standard deviation of the sampling distribution of X¯. 3 A. Sivathayalan, M. Nasari, Z. Montazeri (b)[2] Find the probability that the average score of this group of students is higher than 76. (c)[3] Find the probability that the sample mean deviates from the population mean by less than 2. (d)[4] Construct a 98% confidence interval for µ, the true mean test score.

Explanation / Answer

a)

mean = 75

standard deviation = srqt (16 / 100) = 0.4

b)

P( z > 76-75 / 0.4 )

P( z > 2.5 ) = 0.00621

c)

P( z < -2/0.4)

P( z < -5 ) = 0.000001

d)

alpha = 1 - 0.98 =0.02

alpha / 2 = 0.01

Z = 2.32

I: 75 +/- 2.32 * srqt( 16/100)

75 +/- 0.928

74.072 < miu < 75.928

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