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vichka [17]
2 years ago
15

Suppose X has a continuous uniform distribution over the interval [1.3, 6.2]. Round your answers to 3 decimal places.

Mathematics
1 answer:
goldenfox [79]2 years ago
5 0

Answer:

(a) 3.75

(b) 2.00083

(c) 0.4898

Step-by-step explanation:

It is provided that X has a continuous uniform distribution over the interval [1.3, 6.2].

(a)

Compute the mean of X as follows:

\mu_{X}=\frac{a+b}{2}=\frac{1.3+6.2}{2}=3.75

(b)

Compute the variance of X as follows:

\sigm^{2}_{X}=\frac{(b-a)^{2}}{12}=\frac{(6.2-1.3)^{2}}{12}=2.00083

(c)

Compute the value of P(X < 3.7) as follows:

P(X < 3.7)=\int\limits^{3.7}_{1.3}{\frac{1}{6.2-1.3}}\, dx\\\\=\frac{1}{4.9}\times [x]^{3.7}_{1.3}\\\\=\frac{3.7-1.3}{4.9}\\\\\approx 0.4898

Thus, the value of P(X < 3.7)  is 0.4898.

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Fred buys flags from a manufacturer for f dollars each and then sells the flags in his store for a 26%markup.
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Answer:

the markup is 1.26 (the amount added is .26)

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1.26(40)

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50.4-40

$10.40 is the markup

Step-by-step explanation:

The 26% markup means that he is selling the flags 26% above the cost.

So, the cost would represent 100%, which is 1, and 26% of markup in decimal number is 0.26.

The price including the markup would be 1.26 as decimal or 126% as percentage.

The problem states that the cost is unknown, so we represent that with a variable x. The retail price would be 1.26x, which is 126% per flag.

Finally, if Fred paid $40 per flag, the actual retail price would be:

1.26($40)=$50.40.

With $10.40 of markup.

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Answer:

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