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 500 and the standard deviation is 107. Assume the variable x is normally distributed. left parenthesis a right parenthesis What percent of the SAT verbal scores are less than 675? left parenthesis b right parenthesis If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550? left parenthesis a right parenthesis Approximately nothing% of the SAT verbal scores are less than 675. (Round to two decimal places as needed.) left parenthesis b right parenthesis You would expect that approximately nothing SAT verbal scores would be greater than 550. (Round to the nearest whole number as needed.)

Explanation / Answer

1) p(x<675)=p(z<(675-500)/107)=p(z<1.64)=0.050503

percent of the SAT verbal scores are less than 675=5.0503%

2)p(x>550)=p(z>(550-500)/(107))=p(z>0.467)=0.297017

no. expected to be greater than 550=1000*0.297017=297.017

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