Test Scores are normally distributed mean 500 standard devia

Test Scores are normally distributed, mean= 500 standard deviation=100

?21% of test scores exceed what value?

Probability that randomly selected person scores between 425 and 575?

Probability that a randomly selected person scores less than 500?

Probability that a randomly selected person scores 625 or more?

Need explanation of how to do the steps. Reference to any other example questions and best formulas to use would be helpful. Do I use the formula for standard deviation of a discrete random variable?

Solution

?21% of test scores exceed what value?

P(X>x)=0.21

--> P((X-mean)/s <(x-500)/100) =1-0.21=0.79

--> P(Z<(x-500)/100)=0.79

--> (x-500)/100= 0.81 (from standard normal table)

So x= 500+0.81*100=581

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Probability that randomly selected person scores between 425 and 575?

P(425<X<575) = P((425-500)/100 <Z<(575-500)/100))

=P(-0.75<Z<0.75) = 0.5467 (from standard normal table)

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Probability that a randomly selected person scores less than 500?

P(X<500)= P(Z<(500-500)/100))

=P(Z<0) = 0.5(from standard normal table)

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Probability that a randomly selected person scores 625 or more?

P(X>625) = P(Z>(625-500)/100))

=P(Z>1.25) = 0.1056 (from standard normal table)