# A problem on statistics

stonecoldgen

## Homework Statement

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.

## Homework 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

## 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

Mentor

## Homework Statement

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.

## Homework 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

## 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
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?