MATH SOLVE

2 months ago

Q:
# The automatic opening device of a military cargo parachute has been designed to open when the parachute is 195 m above the ground. suppose opening altitude actually has a normal distribution with mean value 195 and standard deviation 33 m. equipment damage will occur if the parachute opens at an altitude of less than 100 m. what is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes? (round your answer to four decimal places.)

Accepted Solution

A:

The question is posed in terms of damage to equipment, but must be worked by considering the probability the equipment is undamaged. It is worked in two steps.

In the first step, we find the probability that the equipment is dropped undamaged. That is, the probability that the parachute opens at an altitude of 100 m or more given the opening altitude has a normal distribution with ΞΌ=195 m and Ο=33 m. That probability can be found using a suitable calculator or table to be about 0.998004.

In the second step, we find the complement of the probability that 5 parachutes will open properly. This is ...

Β 1 - 0.998004^5 β 0.009940.

The probability that one or more of 5 equipment drops will result in damaged equipment is about 0.0099.

In the first step, we find the probability that the equipment is dropped undamaged. That is, the probability that the parachute opens at an altitude of 100 m or more given the opening altitude has a normal distribution with ΞΌ=195 m and Ο=33 m. That probability can be found using a suitable calculator or table to be about 0.998004.

In the second step, we find the complement of the probability that 5 parachutes will open properly. This is ...

Β 1 - 0.998004^5 β 0.009940.

The probability that one or more of 5 equipment drops will result in damaged equipment is about 0.0099.