Question

For a recent 10k run the finishers are normally distributed with mean 62 minutes and standard deviation 11 minutes.
a) determine percentage of people that finished between 45 and 75 minutes
b) Percentage of finishers less than 80 minutes
c) Obtain the 35th percentile
d) find the eight decile for finishing times

Formula
Raw Score-Mean/Standard deviation = zscore

Answer 1

Can you calculate the z-scores for 45 and 75 minutes using the given formula?

Answer 2

yeah! for 45 it is 0.06057
and for 75 it is .88100

Answer 3

I know B so I just need help with the other ones!

Answer 4

The way the formula is written is ambiguous. This is the formula to use:
\[z=\frac{raw\ score-mean}{standard\ deviation}\]
Can you now calculate the z-scores for 45 and 75 minutes?

Answer 5

so 45-62 and then divide it by 11? Then I just find that number on the zscore chart?

Answer 6

So I got A and B correct!! I just need help with the last two now!
The formula for the 35th percentile is \[\mu+ Z \times \sigma=X\]

Answer 7

From a standard normal distribution table, the z-score for a cumulative probability of 0.35 is -0.385. The 35th percentile is found from
\[X=62+(-0.385\times 11)=you\ can\ calculate\]