Thread: Probability with Normal Distribution

Hi

The automatic opening device of a military cargo parachute has been designed to open when the parachute is 200m above the ground. Suppose opening altitude actually has a normal distribution with mean value 200m and standard deviation 30m. Equipment damage will occur if the parachute opens at an altitude of less than 100m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

How can I set this up in order to solve it?

Originally Posted by shogunhd

Hi

The automatic opening device of a military cargo parachute has been designed to open when the parachute is 200m above the ground. Suppose opening altitude actually has a normal distribution with mean value 200m and standard deviation 30m. Equipment damage will occur if the parachute opens at an altitude of less than 100m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

How can I set this up in order to solve it?

Let X be the random variable height that parachute opens (metres).
Find Pr(X < 100). Without knowing how you've been taught to do this (tables, calculator etc) I can't tell you how to do this. Let the answer be p.

Now let Y be the random variable number of payloads that are damaged.
Y follows a binomial distribution with n = 5 and p = Pr(X < 100).

Find Pr(Y > 0) = 1 - Pr(Y = 0).

Originally Posted by shogunhd

Hi

The automatic opening device of a military cargo parachute has been designed to open when the parachute is 200m above the ground. Suppose opening altitude actually has a normal distribution with mean value 200m and standard deviation 30m. Equipment damage will occur if the parachute opens at an altitude of less than 100m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

How can I set this up in order to solve it?

In two steps:

1. Find the probability that a single parachute will open without equipment damage. Call this value p.

2. Then the probability that there is equipment damage to at least one of five payloads is

1 - Pr(no equipment damage to 5 payloads) = 1 - p^5.