Question

Given a random variable having the normal distribution with mean ? = 7 and ?² = 49, find the probabilities that it will take on a value:

a) greater than 6

b) less than 2

c) between 6 and 18.8

Answer 1

Solution :

Given that ,

mean = = 7

standard deviation = = 7

a)

P(x > 6) = 1 - P(x < 6)

= 1 - P((x - ) / < (6 - 7) / 7)

= 1 - P(z < -0.14)

= 1 - 0.4443   

= 0.5557

Probability = 0.5557

b)

P(x <2) = P(x < 2)

= P((x - ) / < (2 - 7) / 7)

= P( z < -0.71)

= 0.2389

Probability = 0.2389

c)

P( 6 < x < 18.8 ) = P( (6 - 7)/7 < (x - ) / < (18.8 - 7) / 7)

= P(-0.14 < z < 1.69)

= P(z < 1.69) - P( z < -0.14)

= 0.9545 - 0.4443

= 0.5102

Probability = 0.5102