Question

Given that X is a normally distributed random variable with a mean of 50 and a...

Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.

0.7104

0.6680

0.9772

0.9104
Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that ,

mean = = 50

standard deviation = = 2

P(47< x <54 ) = P[(47-50) /2 < (x - ) / < (54-50) /2 )]

= P( -1.5< Z <2 )

= P(Z < 2) - P(Z < -1.5)

Using z table   

= 0.9772 -0.0668

=0.9104

   probability= 0.9104

  
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