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Licemer1 [7]
3 years ago
12

A car painting company has determined that the painting time of cars is uniformly distributed between 25 and 105 minutes. What i

s the probability that it will take between 40 and 65 minutes for that company to paint a car
Mathematics
1 answer:
Masteriza [31]3 years ago
4 0

Answer:

P=\frac{5}{16}

Step-by-step explanation:

For a uniform distribution we have to:

P (X\leq x) =\frac{x-a}{b-a}   for x∈ (a, b)

P (X\leq x) =0}   for x\leq a

P (X\leq x) =1}   for x\geq b

In this case we have to:

a = 25 min and b = 105 min

We want to find:

P (40 \leq X \leq 65)

Then

P (x_1 \leq X \leq x_2) = P(X \leq x_2) - P(X \leq x_1)

P (x_1 \leq X \leq x_2)= \frac{x_2 -x_1}{b-a}

In this case:

x_2 = 65\\\\x_1=40

Therefore:

P (40 \leq X \leq 65)=\frac{65 -40}{105-25}

P (40 \leq X \leq 65)=\frac{25}{80}

P (40 \leq X \leq 65)=\frac{5}{16}

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