# Thread: Normal distribution

1. ## Normal distribution

A container of 20ft carry a weight that is normally distributed with a mean of 5000 t and a standard deviation of 400 t. What percentage of container weight between 5400 and 5600 t?

This is where I reached, how should I conclude on the percentage?
For χ = 5400
Z5400 = (5400-5000)/400
Z5400 = 10
For χ = 5600
Z5600 = (5600-5000)/40
Z5600 = 15

2. ## Re: Normal distribution

First you need to check your calculations.

3. ## Re: Normal distribution

Thank you. Corrected as;
For χ = 5400
Z5400 = (5400-5000)/400
Z5400 = 1
For χ = 5600
Z5600 = (5600-5000)/400
Z5600 = 1.5

4. ## Re: Normal distribution

Good.

P(1<Z<1.5) = P(Z<1.5) - P(Z<1).

Do you understand why and can you find these probabilities?

5. ## Re: Normal distribution

here is where I get confusion, distribution table I have I read for example from z column down to locate 1.5 and I get 0.4332 and for 1 0.3413. Help me how to read the values of 1.5 and 1

6. ## Re: Normal distribution Originally Posted by benedec here is where I get confusion, distribution table I have I read for example from z column down to locate 1.5 and I get 0.4332 and for 1 0.3413. Help me how to read the values of 1.5 and 1
Those will do but they are P(0<Z<1.5) and P(0<Z<1).

The answer you need is still the difference between these two values.

7. ## Re: Normal distribution

was worried probably i read the table incorrectly, the difference i get is this; P(1<Z<1.5) = P(Z<1.5)  P(Z<1) = 0.4332  0.3413 = 0.0919 = 9.19%

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