# Standard normal distrubition

Let X be a random variable of a normal distribution with mean = 42.2 and SD = 3. Find the probability

c)P( 41.2 < X < 46.3)

### 1 Answer

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- 知足常樂Lv 76 years agoFavorite Answer
X ~ N(42.2, 3²)

Pr( 41.2 < X < 46.3)

= Pr( 41.2 - 42.2 < X - 42.2 < 46.3 - 42.2 )

= Pr( (41.2 - 42.2)/3 < (X - 42.2)/3 < (46.3 - 42.2)/3 )

= Pr( -1/3 < (X - 42.2)/3 < 4.1/3 )

= Pr( -1/3 < Z < 4.1/3 ) where Z ~ N(0, 1)

= Pr( -0.333333333 < Z < 1.36666666 )

≈ Pr( -0.33 < Z < 1.37 )

= Pr( 0 < Z < 1.37 ) + Pr( 0 < Z < 0.33 )

= 0.4147 + 0.1293 [from standard normal distribution table]

= 0.544

Excel gives you a more accurate answer as 0.544693755.

=NORM.DIST(46.3,42.2,3,TRUE)-NORM.DIST(41.2,42.2,3,TRUE)

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