Question

Assume that the random variable X is normally distributed, with mean μ = 80 and standard deviation σ = 10. Compute the probability P(95 < X <100).

Answers:

a) 0.1093

b) 0.0823

c) 0.0441

d) 0.0606

Answer 1

Solution :

Given that ,

mean = = 80

standard deviation = = 10

P(95 < X <100 ) = P[(95 - 80) /10 < (x - ) / < (100 - 80) /10 )]

= P( 1.5< Z <2 )

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

Using z table ( see the z value 2 in standard normal (z) table corresponding value is 0.9772) and ( see the z value 1.5 in standard normal (z) table corresponding value is 0.9332 )

=0.9772 -0.9332

=0.0441

probability=0.0441

correct option C