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 509 and the standard deviation is 122. Assume the variable x is normally distributed (a) What percent of the SAT verbal scores are less than 675? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525? (a) Approximately 1% of the SAT verbal scores are less than 675 Round to two decimal places as needed.) SAT verbal scores would be greater than 525 Round to the nearest whole number as b) You would expect that approximately needed.)

Explanation / Answer

= 509 = 122

(a) Z = (x - ) /

x < 675

Z < (675 - 509) / 122

=> Z < 1.3607

=> P(Z < 1.3607) = 0.9132.

=> 91.32%.

(b) Z = (x - ) /

x > 525

Z > (525 - 509) / 122

=> Z > 0.1311

=> P(Z > 1.3607) = 0.4478.

1000 * 0.4478 = 447.8 = 448.

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