Question

Traveling between two campuses of a university in a city via shuttle bus takes, on average, 28 minutes with a standard deviation of 5 minutes. In a given week, a bus transported passengers 40 times. What is the probability that the average transport time was less than 30 minutes?

Answer 1

$\bar{x} = 28$ , $\sigma = 5$ , $n=40$

find $P(\bar{X<30})$

now we calculate value of z by central limit theorem

$z=\frac{(\bar{X}-\bar{x})}{\frac{\sigma}{\sqrt{n}}}=\frac{30-28}{\frac{5}{\sqrt{40}}}=2.53$

the value of z to the left = 0.9943

$P(\bar{X}< 30)= P(Z < 2.53) =0.9943$