Question

The time X a vehicle takes to go through a certain tunnel has mean μ = 12.1 minutes and standard deviation σ = 3.8 minutes. Engineers have estimated that for safety reasons, vehicles should spend on average between 11 and 13 minutes in the tunnel. Assume that there are 50 cars in the tunnel. What is the probability that the mean time X ̄ that these cars will spend on the tunnel is between 11 and 13 minutes?

Answer 1

Given,

population mean $\mu=12.1 min$

Population standard deviation , $\sigma=3.8 min$

Probability that the mean time $\bar{X}$ that these cars will spend on the tunnel is between 11 and 13 minutes is-

$P(11<X<13)=P(\dfrac{11-12.1}{3.8}<z<\dfrac{13-12.1}{3.8})=P(-0.29<z<0.24)=0.2089$