Question

Use the table of standard normal probabilities (z table) to answer the following questions.

1. What is P(z >2.5)?
2. What is P(-0.8 < z < 1.5)?
3. What is P(0.65< z < 1.36)?  
4. What z-value leaves 80 % of the normal distribution to its right?
5. What z-value, and its negative, leaves 10 % of the normal distribution in each tail (a total of 20% of the distribution in both tails combined)?

       

Answer 1

This is a normal distribution question with


a) z = 2.5
This implies that
P(z > 2.5) = 0.0062

b)
z1 = -0.8
z2 = 1.5
This implies that


c)
z1 = 0.65
z2 = 1.36
This implies that



d) Given in the question that 80% of the distribution are to the right, so we are using p = 0.2 (corresponding to 20% of the distribution to the left)
P(X < x) = 0.2
This implies that
P(Z < -0.8416212335729142) = 0.2
z = -0.8416212335729142


e) Given in the question, 10% in each tail means
we will find the values corresponding to p = 0.1 and p = 0.9
P(X < x) = 0.1
This implies that
P(Z < -1.2815515655446004) = 0.1
z = -1.2815515655446004


P(X < x) = 0.9
This implies that
P(Z < 1.2815515655446004) = 0.9
z = 1.2815515655446004

PS: you have to refer z score table to find the final probabilities.
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