Find the area as well please. The national average SAT score (for verbal and mat

Question

Find the area as well please.

The national average SAT score (for verbal and math) is 1028. Suppose that nothing is known about the shape of the distribution and that the standard deviation is 100. Round the final answer to four decimal places and intermediate:-value calculations to two decimal places. Source: New York Times Almanac. If a random sample of 230 scores was selected, find the probability that the sample mean is 1043 or more. Assume that the sample is taken from a large population and the correction factor can be ignored. P(X > 1043) =

Explanation / Answer

mean = 1028 , s = 100 , n = 230 , x = 1043

z = ( x - mean) / ( s / sqrt(n))

= ( 1043 - 1028) /( 100/ sqrt(230))

= 2.27

we need to find P( Z > 2.27)

P(X > 1043) = P( Z > 2.27)= 0.0114

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