Question

The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 40 minutes?

Answer 1

The probability is
`P(X > x) = 0.0013499`

Explanation:

From the question we are told that

The mean is
`\mu = 25`

The standard deviation is
`\sigma = 5 \ minutes`

The random number
`x = 40`

Given that the time taken is normally distributed the probability is mathematically represented as

`P(X > x) = P[(X -\mu)/(\sigma ) > (x -\mu)/(\sigma ) ]`

Generally the z-score for the normally distributed data set is mathematically represented as

`z = (X - \mu)/(\sigma )`

So

`P(X > x) = P[Z > (40 -25)/(5 ) ]`

`P(X > x) = 0.0013499`

This value is obtained from the z-table