core: 0 of 1 pt | 50f 9 (4 complete) HW Score: 44.44%, 4 of 9 pts Question Help

Question

core: 0 of 1 pt | 50f 9 (4 complete) HW Score: 44.44%, 4 of 9 pts Question Help * Use the normal distribution of SAT critical reading scores for which the mean is 511 and the standard deviation is 123. Assume the variable x is normally distributed (a) What percent of the SAT verbal scores are less than 675 (b 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550? (a) Approximately[1%of the SAT verbal scores are less than 675. Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer Clear All Check Answer MacBook Ai

Explanation / Answer

Solution:- Given that mean = 511 , sd 123
a) P(X < 675) = P(Z < (X - mean)/sd)
= P(Z < (675 - 511)/123)
= P(Z < 1.3333)
= 0.9082
= 90.82%
  
=> Approximately 90.82% of the SAT verbal scores are less than 675.

b) P(X > 550) = P(Z > (X - mean)/(sd/sqrt(n))
= P(Z > (550 - 511)/(123/sqrt(1000))
= P(Z > 10.0267)
= 0

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