statistics and probability

Question

1. Assume that X has a normal distribution with the specified mean and standard deviation.
2. mean=6; standard deviation=0.2
3. Find the 62nd percentile, that is the cutoff value of the bottom 62%. Round z-score and your answer to 3 decimal places.

Answer 1

Hi Fatmata,

This problem uses the classic equation in introductory statistics:

z=(x-mu)/sigma

Breaking this down:

z=z-score

x=x, value you are looking for

mu=mean

sigma=standard deviation

Now, for this problem, you were given a proportion (the percentile) and asked to find the x-value, not the other way around. This means we need to look at the interior of the z-table to find the closest value to 0.62.

This falls between 0.6179 and 0.6217. Looking at the left column and top row, corresponding z falls between 0.30 and 0.31. 0.62 is closer to 0.6217 than 0.6179, so we'll go with 0.306 for 3 decimals. Statistical software will provide a more exact z-score.

Thus:

z_0.62=0.306

x=x

mu=6

sigma=0.2

Substituting:

0.306=(x-6)/0.2

0.061=x-6

x=6.061

Final answer may vary due to use of software. I hope this helps.