Question

at one high school, the mean time for running the 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. the times are very closely approximated by a normal curve. find the percent of times that are at least 14.3 seconds

Answer 1

Answer:

The percent of times that are at least 14.3 seconds is approximately 16%.

Step-by-step explanation:

Let X denote the time for running the 100-yard dash.

It is provided that the times are very closely approximated by a normal curve.

So, the random variable X follows a normal distribution with a mean time of 15.2 seconds and with a standard deviation of 0.9 seconds.

Compute the probability of times that are at least 14.3 seconds as follows:

$P(X\geq 14.3)=P(\frac{X-\mu}{\sigma}\geq \frac{14.3-15.2}{0.9})$

                    $=P(Z\geq -1)\\\\=1-P(Z<-1)\\\\=P(Z<-1)\\\\=0.15866\\\\\approx 0.159$

*Use a z-table.

Thus, the percent of times that are at least 14.3 seconds is approximately 16%.