Mathematics, 30.07.2021 01:50 kimjooin02

The automatic opening device of a military cargo parachute has been designed to open when the parachute is 185 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 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

Answers: 1

Show answers

Answers

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Step-by-step explanation:

For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.

To find the probability of damage on a parachute, the normal distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability of a parachute having damage.

The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that $\mu = 185, \sigma = 32$

Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of Z when X = 100. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{100 - 185}{32}$

Z = -2.66

Z = -2.66 has a p-value of 0.0039.

What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

0.0039 probability of a parachute having damage, which means that p = 0.0039

5 parachutes, which means that n = 5

This probability is:

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807$

Then

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193$

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Answer from: Quest

5 cm

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

$\dfrac{x}{40}=\dfrac{4}{32}$ cross multiply

$32x=(40)(4)$

$32x=160$ divide both sides by 32

$x=5$

Question 3 what is the value of x? cm 3 cm 4 cm 5 cm 4.5cm

Answer from: Quest

step-by-step explanation:

its 512 because parenthesis and to the 2nd power is 512 so it will be 512

Answer this question for 50 points and brainliest : d

Another question on Mathematics

Mathematics, 21.06.2019 18:00

What are the equivalent ratios for 24/2= /3= /5.5=108/ = /15

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

The given dot plot represents the average daily temperatures, in degrees fahrenheit, recorded in a town during the first 15 days of september. if the dot plot is converted to a box plot, the first quartile would be drawn at __ , and the third quartile would be drawn at link to the chart is here

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

What is the value of x in the equation 2(x-4) = 4(2x + 1)?

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

If you were constructing a triangular frame, and you had wood in the length of 4inches, 4 inches, and 7 inches, would it make a triangle? would you be able to create a frame from these pieces of wood? yes or no. explain your mathematical thinking

Answers: 2

Answer

You know the right answer?

The automatic opening device of a military cargo parachute has been designed to open when the parach...

Questions