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In: Statistics and Probability

SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of...


SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). If a sample of 35 students are selected randomly, find the probability that the sample mean is above 470.

A.) 0.244

B.) 0.9756

C.) 0.0445

D.) 0.0244

Solutions

Expert Solution

Solution :

Given that ,

mean = = 430

standard deviation = = 120

n = 35

=   = 430

= / n = 120/ 35  = 20.2837

P( > 470 ) = 1 - P( < 470 )

= 1 - P[( - ) / < (470 -430) /20.2837 ]

= 1 - P(z < 1.97 )

= 1 - 0.9721 = 0.0244

PROBABILITY = 0.0244

Probability =

orchestra answered 2 years ago
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