when ian runs the 400 meter dash, his finishing times are normally distributed with a mean of 71 seconds and…
when ian runs the 400 meter dash, his finishing times are normally distributed with a mean of 71 seconds and a standard deviation of 2.5 seconds. if ian were to run 23 practice trials of the 400 meter dash, how many of those trials would be faster than 74 seconds, to the nearest whole number?
Answer
Explanation:
Step1: Calculate the z - score
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 74$, $\mu=71$, and $\sigma = 2.5$. $z=\frac{74 - 71}{2.5}=\frac{3}{2.5}=1.2$
Step2: Find the probability of $z>1.2$
Using the standard normal distribution table, the probability of $z\leq1.2$ is $0.8849$. So the probability of $z > 1.2$ is $P(Z>1.2)=1 - 0.8849 = 0.1151$.
Step3: Calculate the number of trials
Multiply the probability by the number of trials $n = 23$. Number of trials $=0.1151\times23\approx2.6573\approx3$
Answer:
3