Question

Let X be a random variable which follows normal distribution with mean 12 and variance 0.25. Then find the following probabilities

(a) P( X  ≤ 15 )

(b) P( X  ≤ 17.5 )

(c) P( |X-15| ≤ 3 )

                        

  

                     

Answer 1

Given

mean = = 12

variance = 0.25

standard deviation = =   = 0.5

a)

P(x 15) =

P((x - ) / (15 - 12) / 0.5)

= P(z 6)

Using standard normal table,

P(x 15) = 0.0000

b)

P( X  ≤ 17.5 ) =

P((x - ) / (17.5 - 12) / 0.5)

= P(z 11)

Using standard normal table,

P(x 17.5) = 0.0000

c)

P( |X-15| ≤ 3 ) =

P(-3   x - 12 3) = P(-9 x 15)

= P((-9 - 12) / 0.5 z (15 - 12) / 0.5)

= P(-42 z 6) = P(z 6) - P(z -42)

= 0.0000 - 0.0000

P( |X-15| ≤ 3 ) = 0

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