when gabriel runs the 400 meter dash, his finishing times are normally distributed with a mean of 63 seconds…
when gabriel runs the 400 meter dash, his finishing times are normally distributed with a mean of 63 seconds and a standard deviation of 0.5 seconds. if gabriel were to run 25 practice trials of the 400 meter dash, how many of those trials would be slower than 64 seconds, to the nearest whole number? statistics calculator
Answer
Explanation:
Step1: Calculate the z - score
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 64$, $\mu=63$, and $\sigma = 0.5$. $z=\frac{64 - 63}{0.5}=\frac{1}{0.5}=2$
Step2: Find the probability using the standard normal distribution
Looking up the z - score of 2 in the standard - normal distribution table, the area to the left of $z = 2$ is approximately $0.9772$. This means the probability that a single trial has a time less than 64 seconds is $P(X<64)=0.9772$.
Step3: Calculate the number of trials slower than 64 seconds
We have 25 practice trials. The number of trials slower than 64 seconds is $n = 25\times(1 - 0.9772)$. $n=25\times0.0228 = 0.57\approx1$
Answer:
1