Question

When Lillian runs the 400 meter dash, her finishing times are normally distributedwith a mean of 78 seconds and a standard deviation of 2.5 seconds. If Lillian were torun 42 practice trials of the 400 meter dash, how many of those trials would beslower than 83 seconds, to the nearest whole number?

Answer 1

The normal distribution mentioned in the problem can be understood as a function f(t) where t is in seconds.

We need to find the Z-score formula shown below

`Z=(x-\mu)/(\sigma)`

Where mu is the mean and sigma is the standard deviation.

In our case,

`\begin{gathered} x=83,\mu=78,\sigma=2.5 \\ \Rightarrow Z=(83-78)/(2.5)=(5)/(2.5)=2 \end{gathered}`

The corresponding probability to a Z-score equal to 2 can be found using a Z-score table. Z=2 -> 0.9972

Then, the answer is

`42\cdot0.9972=41.8824\approx42`

Then, the answer is approximately 42 trials