Question

Let x be a continuous random variable that is normally distributed with mean 73 and std. deviation 14. Sketch & shade the curves and find the probabilities that x assumes a value:
a. less than 51           b. greater than 72

Answer 1

Solution :

Given that,

mean = = 73

standard deviation = = 14

P(X<51 ) = P[(X- ) / < (51-73) /14 ]

= P(z <-1.57 )

Using z table

probability = 0.0582

b

P(X> 72 ) =1 - P[(X- ) / < (72-73) /14 ]

= 1 -P(z <-0.07 )

Using z table

=1-0.4721

probability = 0.5279