Inverse Normal / Quantile Problem

Find a threshold value (time, amount, mass, etc.) such that a given probability condition is met, e.g., find m such that P(X ≥ m) = 0.99 or find the departure time ensuring on-time arrival with probability 0.9.

bac-s-maths 2014 Q1B View
We assume in this part that the student uses the bicycle to go to his school. When he uses the bicycle, his travel time, expressed in minutes, between his home and his school is modeled by a random variable $T$ which follows a normal distribution with mean $\mu = 17$ and standard deviation $\sigma = 1.2$.
  1. Determine the probability that the student takes between 15 and 20 minutes to get to his school.
  2. He leaves his home by bicycle at 7:40 a.m. What is the probability that he is late for school?
  3. The student leaves by bicycle. Before what time must he leave to arrive on time at school with a probability of 0.9? Round the result to the nearest minute.
bac-s-maths 2015 Q1B2 View
According to a statistical study conducted over several months, it is assumed that the number $X$ of budget padlocks sold per month in the hardware store can be modeled by a random variable that follows a normal distribution with mean $\mu = 750$ and standard deviation $\sigma = 25$.
The store manager wants to know the number $n$ of budget padlocks he must have in stock at the beginning of the month, so that the probability of running out of stock during the month is less than 0.05. The stock is not replenished during the month.
Determine the smallest integer value of $n$ satisfying this condition.
bac-s-maths 2017 Q1A View
Part A
As part of its activity, a company regularly receives quotation requests. The amounts of these quotations are calculated by its secretariat. A statistical study over the past year leads to modelling the amount of quotations by a random variable $X$ which follows the normal distribution with mean $\mu = 2900$ euros and standard deviation $\sigma = 1250$ euros.
  1. If a quotation request received by the company is chosen at random, what is the probability that the quotation amount exceeds 4000 euros?
  2. In order to improve the profitability of its activity, the entrepreneur decides not to follow up on $10\%$ of requests. He discards those with the lowest quotation amounts. What must be the minimum amount of a requested quotation for it to be taken into account? Give this amount to the nearest euro.