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The combined SAT scores for the students at a local high school are normally distributed with a mean of 1527 and a standard deviation of 291. The local college includes a minimum score of 1207 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement? P(X > 1207) =

Respuesta :

Answer:

Step-by-step explanation:

Let x be the random variable representing the SAT scores for the students at a local high school. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 1527

σ = 291

the probability to be determined is expressed as P(x > 1207)

P(x > 1207) = 1 - P(x ≤ 1207)

For x < 1208

z = (1207 - 1527)/291 = - 1.1

Looking at the normal distribution table, the probability corresponding to the z score is 0.16

P(x > 1207) = 1 - 0.16 = 0.84

Therefore, the percentage of students from this school earn scores that satisfy the admission requirement is

0.84 × 100 = 84%

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