# Thread: Statistics question - I think it is about a z test

1. ## Statistics question - I think it is about a z test

Sorry, but this is too difficult. I need to work on my calculator, but I am not confident how:

The weights, in kg, of men in a random sample from a given population can be modelled by a normal distribution with mean 83.5 and 16.8.

a) What is the value above which 20% of the weights of men from the population will lie?

b) What is the range of values, symmetric about the mean, within which approx 95% of the weights of men will lie?

c) What is the percentage of weights of men above 100 kg.

2. Originally Posted by dolkam
Sorry, but this is too difficult. I need to work on my calculator, but I am not confident how:

The weights, in kg, of men in a random sample from a given population can be modelled by a normal distribution with mean 83.5 and 16.8.

a) What is the value above which 20% of the weights of men from the population will lie?

b) What is the range of values, symmetric about the mean, within which approx 95% of the weights of men will lie?

c) What is the percentage of weights of men above 100 kg.
You just need to confirm whether 16.8 is the variance or the standard deviation.

Then you work with the Z-tables, using $\displaystyle\ Z=\frac{x-\mu}{\sigma}$

where x is weight, $\mu$ is the mean and $\sigma$ is the standard deviation.

$x=Z\sigma+\mu$

For (a) you need to find the value of Z corresponding to a probability of 0.8,
since 80% of the bell-shaped curve lies below that.

For (b) you need the values of Z corresponding to 2.5% and 97.5%

since a symmetrical 95% of the graph lies in between (twice 47.5%).

For part (c) you must calculate Z corresponding to x=100kg, using the formula given above..

then read off the probability from the tables.
That will give you the probability of a weight being below 100kg.
Subtract from 1 and multiply by 100 to get the percentage.

3. Thanks you to Archie. I can finish this now. It is not so bad when you explained it! Sometimes it is difficult to find where I have to place the numbers in the question. Now I know. Thanks.