# A problem on statistics

1. Oct 11, 2011

### stonecoldgen

1. The problem statement, all variables and given/known data

An airline flies the same route at the same time each day. The flight time varies according to a Normal distribution with unknown mean and standard deviation. On 15% of days, the flight takes more than an hour. On 3% of days, the flight lasts 75 minutes or more. Use this information to determine the mean and standard deviation of the flight time distribution.

2. Relevant equations

well, i can use the normalcdf, normalpdf and invNorm on the TI, but i'm not sure how, since to use them, i need the standard deviation and the mean

3. The attempt at a solution

what i have attempted is using those tools on the calculator, but it doesn't really get you to anything

2. Oct 11, 2011

### Staff: Mentor

Some tools you should be using before you start in with the calculator are a pencil and some paper, and a table of values of the standard normal distribution.

You are given that the flight times are normally distributed, with mean $\mu$ and standard deviation $\sigma$, both unknown.

Let X be the normally distributed random variable that represents flight times.

You are given that Pr(X > 60) = .15 and Pr(X > 75) = .03

How can you write these probabilities so that they involve Z, the standard normal random variable? What's the relationship between Z and X?