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 508 and the standard deviation is 109. Assume the variable x is normally distributed. left parenthesis a right parenthesis

(a) What percent of the SAT verbal scores are less than 600?

(b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550?

(a) Approximately % of the SAT verbal scores are less than 600.

(Round to two decimal places as needed.)

(b) You would expect that approximately nothing SAT verbal scores would be greater than 550.

(Round to the nearest whole number as needed.)

Explanation / Answer

Mean = 508

Sd = 109

A) P(X < 600) = P((X - mean) /sd < (600-508)/109)

= P(Z < 0.84)

= 0.7995

B) P(X > 550) = P((X - mean) /sd > (550-508)/109)

= P(Z > 0.39)

= 1 - P(Z < 0.39)

= 1 - 0.6517

= 0.3483

Expected value = 1000 * 0.3483 = 348

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