SOLUTION: Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112. If 1 man is randomly selected, find the probabi

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Question 879645: Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112.
If 1 man is randomly selected, find the probability that his score is at least 574.5
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Population: mean = 509, sd = 112

*Note: z+=+blue%28x+-+mu%29%2Fblue%28sigma%29

P(x ≥ 574.6)= 1 - P( z ≤ 65.6/112)= 1 - P(z ≤ .5857) = 1-.7210 = .2790  0r 27.9% chance



For the normal distribution: Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Area under the standard normal curve to the left of the particular z is P(z)

Note: z = 0 (x value: the mean) 50% of the area under the curve is to the left and 50%  to the right