SOS- Need help on Maths Qn

yourfavouritefriend SG

Hi friends,

can any one advise the following qn-

Given than Z ~ N (0, 1), find the value of a if

a) P (Z > a)= 0.0838

b) P (Z > a) = 0.9898

c) P (Z < a) = 0.0009

d) P (Z < a) = 0.881

This qn might need some sort of tables (standard normal distribution) etc or to draw some sorts of graphs. Please advise how to do the qn

Thanks

wee_ws SG

Hi,

If you are using a table that considers the left region, carry out these steps:

1. Convert P(Z > a) to the P(Z < a) form, e.g.,

P(Z > a) = 0.0838 becomes P(Z < a) = 1 - 0.0838 = 0.9162.

2. Search for the probability value in the table, e.g., 0.9162.

3. Identify the row and column values corresponding to the probability value, e.g., 1.3 is the row value and 8 is the column value corresponding to 0.9162.

4. a is made up of these two values, e.g., a = 1.38.

If you have a graphic calculator, it'll be much easier to find the value of a. Thanks.

Cheers,
Wen Shih

yourfavouritefriend SG

Do I need to draw any graphs for the qns?

wee_ws SG

Hi,

The graph is not necessary, unless you wish to draw it to allow you to see which side (left or right) the probability is referring to. Thanks.

Cheers,
Wen Shih

yourfavouritefriend SG

Then how to do Question C & D? I dont understand point number 4( a is made up of these two values, e.g., a = 1.38). finally why do i need to use graphic calculator? and what does Z represent and what is the thing that I need to show in this qn?

wee_ws SG

Hi,

For questions (c) and (d), you just apply steps 2 to 4.

For the example in step 4, a = 1.3 + 0.08.

For A-level, students are expected to use a graphic calculator to find a.

You are just finding the value of a, the z-value such that probability that Z exceeds or is less than a is some value.

Thanks.

Cheers,
Wen Shih