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SAT scores are normally distributed with a mean of 1200 and a variance of 1600. What...

SAT scores are normally distributed with a mean of 1200 and a variance of 1600. What is the probability that a random sample of 16 scores will yield a mean score less than 1192.5?

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Expert Solution

Given that ,

mean = = 1200

variance = 1600

standard deviation = = 1600 = 40

n = 16

= 1200 and

= / n = 40 / 16 = 10

P( < 1192.5) = P(( - ) / < (1192.5 - 1200) / 10) = P(Z< -0.75) = 0.2266

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orchestra answered 1 year ago
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