Mathematics: Find the slope from this graph

Find the slope from this graph - id10404688, cymoneej

kaybaby23

06.07.2022

P(X 7) = 0.5

P(X < 3) = -0.5

$x = 6.2 \ hours$

$x_1 = 8 \ hours$

Mean $\mu = 7$

Standard deviation $s \approx 1.1547$

Step-by-step explanation:

From the question we are told that

The amount of time a repairman needs to fix a furnace is uniformly distributed from 5 and 9 hours

Generally the probability that it takes the repairman more than 7 hours to fix a furnace is mathematically represented as

$P(X 7) = \frac{9- 7}{9-5}$

=> P(X 7) = 0.5

Generally the probability that a randomly selected furnace repair requires less than 3 hours. is mathematically represented as

$P(X < 3) = \frac{3 -5}{9-5}$

=> P(X < 3) = -0.5

Generally the 30th percentile of furnace repair times is mathematically represented as

$30^{th} \ percentile = \frac{x - 5}{9-5}$

=> $0.3 = \frac{x - 5}{9-5}$

=> $x = 6.2 \ hours$

Generally the time taken for the longest 25% of furnace repair is mathematically evaluated as

$75^{th} \ percentile = \frac{x_1 - 5}{9-5}$

Here making use of the $75^{th}$ because we are considering duration that fall with the top $25^{th}$

=> $0.75 = \frac{x_1 - 5}{9-5}$

=> $x_1 = 8 \ hours$

Generally the mean is mathematically represented as

$\mu = \frac{5 + 9 }{2}$

=> $\mu = 7$

Generally the standard deviation is mathematically represented as

$s = \sqrt{ \frac{(9- 5)^2}{12} }$

=> $s \approx 1.1547$

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