Question

The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately Normal with mean ? = 271 and standard deviation ? = 32 . Choose one 12th-grader at random. What is the probability (±0.1, that is round to one decimal place) that his or her score is higher than 271 ? Higher than 367 (±0.0001; that is round to 4 decimal places)? Now choose an SRS of 16 twelfth-graders and calculate their mean score x???. If you did this many times, what would be the mean of all the x???-values? What would be the standard deviation (±0.1; that is round to one decimal place) of all the x???-values? What is the probability that the mean score for your SRS is higher than 271 ? (±0.1; that is round to 1 decimal place) Higher than 367 ? (±0.0001; that is round to 4 decimal places)

Answer 1

a)

mu= 271

sigma= 32

X= 271

Z=(X-mu)/sigma

=(271-271)/32

=0

probability =P(Z>0)

=0.5

for higher than 367

mu= 271

sigma= 32

X= 367

Z=(X-mu)/sigma

=(367-271)/32

=3

probability =P(Z>3)

=0.00135

b)

sample mean=271

sample standard deviation=sigma/sqrt(n)

=32/(sqrt(16))

=32/4=8

now higher than 271

=

=0

required probability =P(Z>0)=0.5

now for higher than 367

=

=12

P(Z>12)=0.0000

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