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 of 300 and standard deviation of 35.a.choose one 12th-grader at random. what is the probability that his or her score is higher than 300? higher than 335?b.now choose an srs of four 12th-graders. what is the probability that their mean score is higher than 300? higher than 335?

z-score is given by:
z=(x-μ)/σ
thus:
a]
 i) P(x>300)
z=(300-300)/35=0
P(x>300)=P(z=0)=0.5

ii) P(x>335)
z=(335-300)/35
z=1
P(x>35)=P(z=1)=0.1587

b] Since we are choosing from the random sample of 4, then first we shall have:
σ/√n
=35/√4=17.5
thus

i] P(x>300)
z=(300-300)/17.5=0
thus:
P(x>300)=P(z=0)=0.5


ii] P(x>335)
z=(335-300)/17.5=2
Thus:
P(x>335)=P(z=2)=0.9772