Question

IfXis a normal random variable with parametersμ= 10 andσ2= 36, compute a)P(X >5) b)P(4< X <8)...

IfXis a normal random variable with parametersμ= 10 andσ2= 36, compute

a)P(X >5)

b)P(4< X <8)

c)P(X <8).

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Given ,

= 10 , = sqrt(36) = 6

we convert this to standard normal as

P( X < x) = P( Z < x - / )

a)

P( X > 5) = P( Z > 5 - 10 / 6)

= P( Z > -0.8333)

= P( Z < 0.8333)

= 0.7977

b)

P( 4 < X < 8) = P( X < 8) - P( X < 4)

= P( Z< 8 - 10 / 6) - P( Z < 4 - 10 / 6)

= P( Z < -0.3333) - P( Z < -1)

= 0.3695 - 0.1587

= 0.2108

c)

P( X < 8) = P (Z < 8 - 10 / 6)

= P (Z < -0.3333)

= 0.3695

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