Question

After the physical training required during World War II, the distribution of mile run times for male students at the University of Illinois was approximately Normal with mean 7.11 minutes and standard deviation 0.74 minutes. What proportion of these students could run a mile in 7 minutes or less?

Answer 1

Answer:

$\frac{1101}{2500}$

Step-by-step explanation:

Given,

Mean, $\mu=7.11$ minutes,

Standard deviation = $\sigma = 0.74$ minutes,

Let x represents the run time,

Thus, the probability of students who could run a mile in 7 minutes or less

= P( x ≤ 7 )

$=P(\frac{x-\mu}{\sigma} \leq \frac{x-\mu}{\sigma})$

$=P(z\leq \frac{7-7.11}{0.74})$

$=P(z\leq -0.15 )$

By the normal distribution table,

$= 0.4404$

$=\frac{4404}{10000}$  

$=\frac{1101}{2500}$

Hence, the proportion of students who could run a mile in 7 minutes or less is about $\frac{1101}{2500}$