question help: Statistic exam now tomorrow: help question by question… - Help.com

I have a lecture slide which claims:

68% of the values will lie within 1 standard deviation of the mean
So between £630 and £1130

95% of the values will lie within 2 standard deviation of the mean
So between £380 and £1380

99.7% of the values will lie within 3 standard deviation of the mean
So between £130 and £1630

shsha wrote:
What’s the formula that give you the percentage when you put in the:* Mean* SD* Cutoff point

Cutoff point?

z=(x-mean)/sd (Sorry I don’ know any conventions for typing formula)

z= (1000-880)/250
Z= 0.48

Yes? No? Maybe?

The answer to this is:

- Draw a diagram!!
- z = (1000-880)/250 = 120/250 = 0.48
- Tables for z=0.48 give .1844
- Required area = 0.5-.1844 = 0.3156

I have a diagram showing the mean in the middle) and the z value I want to find to the right a little with the area between the mean and the z value shaded.

I’ve used the above formula to find the ‘z-value’ (0.48).

So now, what about these tables??

Ok, so I’m going to assume that the Standard Normal Distribution tables will be given in the exam.

So I take my 0.48 and look that up in the table which gives me 0.1844

0.1844 is the area under the curve between the mean and my z value.

So, 18.44% of project costs are between £880 and £1000

Because the data is Normally distributed, 50% of the data MUST be above the mean.
To calculate the percentage of projects that cost more, I take 18.44% away from 50% as to exclude the projects costing between 880 and 1000 to give me 31.56% (or 0.3156).

I think I have that right in my head. Do I write that as 31.56% or 0.3156?

1B: What is the probability that the cost will be between 500 and 600.

So this time I need to work out two z-values…

Work out z values…

z=(x-mean)/sd

z1=(600-880)/250
= -1.12
= 1.12

z2=(500-880)/sd
= -1.92
= 1.52

Look up z value sin table to get area…

z1= 0.3686
z2= 0.4357

As z1 is not relevant to what I’m looking for but is included in z2 I should take z1 from z2:

0.4357-0.3686
=0.0671

So I can conclude that 6.71% of projects are likely to cost between £500 and £600

1C: What is the probability that the project cost will be below £450

z=(x-mean)/sd
=(450-880)/250
=-1.72
= 1.72

z = 1.72 = 0.4573

0.5 - 0.4573
=0.0427

(meaning that 4.273% of projects have cost less than £450

D What cost should be budgeted for so that there is only a 5% chance that the cost will be less than this?