Suppose X is a random variable with mean 10 and variance 9. Then P( 4 < X < 16) is greater than 0.5. True False

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Question 1
Suppose X is a random variable with mean 10 and variance 9. Then P( 4 <X < 16) is greater than 0.5.
True
False
Transcribed Image Text:Question 1 Suppose X is a random variable with mean 10 and variance 9. Then P( 4 <X < 16) is greater than 0.5. True False
Expert Solution
Step 1

Question 1:

Let X is a random variable with mean 10 and variance 9.

The value of P4<X<16 is,

P4<X<16=P4-103<X-μσ<16-103=P-2<z<2=Pz<2-Pz<-2

The probability of z less than –2 can be obtained using the excel formula “=NORM.S.DIST(–2,TRUE)”. The probability value is 0.02275.

The probability of z less than 2 can be obtained using the excel formula “=NORM.S.DIST(2,TRUE)”. The probability value is 0.97725.

The required probability is,

P4<X<16=Pz<2-Pz<-2=0.97725-0.02275=0.9545>0.5

The value of P4<X<16 is 0.9545.

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