Mathematics: SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on the data from the College Board ATP). If a sample of 15 students is selected randomly, find the probability that the sample mean is above 500. Does the central limit theorem apply for this problem?

SAT verbal scores are normally distributed with a

desiree98

13.02.2022

The value is P(X 500 ) = 0.011942

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 430$

The standard deviation is $\sigma = 120$

The sample size is n = 15

Generally the probability that the sample mean is above 500

Gnerally the standard error of mean is mathematically represented as

$s = \frac{\sigma }{ \sqrt{n} }$

=> $s = \frac{ 120 }{ \sqrt{15} }$

=> s = 30.984

Generally the probability that the sample mean is above 500

$P(X 500 ) = P( \frac{X - \mu }{\sigma_x} \frac{500 - 430 }{ 30.984 } )$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

P(X 500 ) = P( Z 2.259 )

=> P(X 500 ) = P( Z 2.259 )

From the z table the area under the normal curve to the right corresponding to 2.259 is

P( Z 2.259 ) = 0.011942

=> P(X 500 ) = 0.011942

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AADJ4

15.08.2020

answer:

Parallel lines never touch.

Perpendicular lines touch at one point which is 90 degrees.

Parallel lines have same slope.

Perpendicular lines have opposite reciprocal slopes.

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