Question

Use a Normal distribution table such as the one located at the link mentioned below to work on
Problems 1, 2 and 3 with N(μ,σ²). Note: the sigma squared. The notation is not universally used the
same. Show the work for your calculations.

http://users.stat.ufl.edu/~athienit/Tables/Ztable.pdf

1-1) Calculate P(X<0.4) if X ~ N(0,1)
1-2) Calculate P(X<0.4) if X ~ N(1,4)
1-3) Calculate P(X>0.4) if X ~ N(1,¼)

Answer 1

1)

Solution :

Given that ,

mean = = 0

standard deviation = = 1

P(x < 0.4) = P((x - ) / < (0.4 - 0) / 1) = P(z < 0.4)

Using standard normal table,

P(x < 0.4) = 0.6554

Probability = 0.6554

2)

Given that ,

mean = = 1

variance = ² = 4

standard deviation = = 2

P(x < 0.4) = P((x - ) / < (0.4 - 1) / 2) = P(z < -0.3)

Using standard normal table,

P(x < 0.4) = 0.3821

Probability = 0.3821

3)

Given that ,

mean = = 1

variance = ² = 1/4

standard deviation = = 1/2 = 0.5

P(x > 0.4) = 1 - P(x < 0.4)

= 1 - P((x - ) / < (0.4 - 1) / 0.5)

= 1 - P(z < -1.2)

= 1 - 0.1151

= 0.8849

P(x > 0.4) = 0.8849

Probability = 0.8849