The relationship between speed, distance and time can be calculated with

Mathematics

1 answer:

Aneli [31]3 years ago

3 0

Answer:

Step-by-step explanation:

105 or D divided by 175 meters per second or T equals .6

105÷175=.6

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Trainees must complete a specific task in less than 2 minutes. Consider the probability density function below for the time it t

antiseptic1488 [7]

Answer:

a) 0.8132 or 81.32%

b) 0.1868 or 18.68%

c) 0.6116 or 61.16%

d) 0.7667 minutes

e) 0.8667 minutes

f) 0.1 minutes

Step-by-step explanation:

If f(x) = 0.85-0.35x (0<x<2) is the PDF and X is the random variable that measures the time it takes for a trainee to complete the task, the probability a trainee will complete the task in less than 1.31 minutes is P(X<1.31)

$\large P(X$

The probability that a trainee will complete the task in more than 1.31 minutes is

P(X>1.31) = 1 - P(X<1.31) = 1 - 0.8132 = 0.1868

The probability it will take a trainee between 0.25 minutes and 1.31 minutes to complete the task is P(0.25<X<1.31)

$\large P(0.25$

the expected time it will take a trainee to complete the task

is E(X)

$\large E(X)=\int_{0}^{2}xf(x)dx=\int_{0}^{2}x(0.85-0.35x)dx=0.85\int_{0}^{2}xdx-0.35\int_{0}^{2}x^2dx=\\\\=0.85*\frac{2^2}{2}-0.35*\frac{2^3}{3}=0.7667\;minutes$

$\large E(X^2)=\int_{0}^{2}x^2f(x)dx=\int_{0}^{2}x^2(0.85-0.35x)dx=0.85\int_{0}^{2}x^2dx-0.35\int_{0}^{2}x^3dx=\\\\=0.85*\frac{2^3}{3}-0.35*\frac{2^4}{4}=0.8667$