Question

Suppose the random variable X follows a normal distribution with mean μ=50and standard deviation σ=10.

Calculate each of the following.

In each case, round your response to at least 4 decimal places.

a) P(X<41)=   

b) P(X>61)=   

c) P(45<X<65)=   

Answer 1

Solution :

Given that ,

mean = = 50

standard deviation = = 10

a) P(x < 41 ) = P[(x - ) / < (41 - 50) / 10 ]

= P(z < -0.90)

Using z table,

= 0.1841

b) P(x > 61) = 1 - p( x< 61)

=1- p P[(x - ) / < (61 - 50) / 10 ]

=1- P(z < 1.10)

Using z table,

= 1 - 0.8643

= 0.1357

c) P(45 < x < 65) = P[(45 - 50)/ 10) < (x - ) /  < (65 - 50) / 10) ]

= P(-0.50 < z < 1.50)

= P(z < 1.50) - P(z < -0.50)

Using z table,

= 0.9332 - 0.3085

= 0.6247