Use the normal distribution of SAT critical reading scores for which the mean is

Question

Use the normal distribution of SAT critical reading scores for which the mean is 510 and the standard deviation is 105. Assume the variable x is normally distributed. (a) What percent of the SAT verbal scores are less than 650? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525? (a) Approximately % of the SAT verbal scores are less than 650. (Round to two decimal places as needed.) (b) You would expect that approximately SAT verbal scores would be greater than 525. (Round to the nearest whole number as needed.)

Explanation / Answer

1) p(x<650)=p(z<(650-510)/105)
=p(z<140/105)
=p(z<1.3333)
  =0.9082

Approximatley 90.82% of the SAT verbal scores are less than 650

b)p(x>525)=p(z>(525-510)/105)
=p(z>15/105)
=p(z>0.1428)
=10.5557
=0.4443

expected to be greater than 525=1000*0.4443=444.3

NO, expect that approximately 444.3 SAT verabl scores would be greater than 525

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