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3 years ago

Brainliest to right answer...

Mathematics

1 answer:

satela [25.4K]3 years ago

8 0

the slope is -2

have a nice day :D

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2 years ago

Consider the following probability distribution function of the random variable X which represents the number of people in a gro

Troyanec [42]

Answer:

(a) 3.55

(b) 3.45 and 1.86

(d) 0.016

Step-by-step explanation:

The random variable <em>X</em> denotes the number of people in a group (party) at a restaurant.

(a)

The formula to compute the mean is:

$\mu=\sum {x\cdot P(X=x)}$

Consider the Excel sheet attached.

The mean is, 3.55.

(b)

The formula to compute the variance is:

$\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}$

Consider the Excel sheet attached.

Compute the variance as follows:

$\sigma^{2}=[\sum {x^{2}\cdot P(X=x)}]-(\mu)^{2}\\\\=16.05-(3.55)^{2}\\\\=3.4475\\\\\approx 3.45$

The variance is, 3.45.

Compute the standard deviation as follows:

$\sigma=\sqrt{\sigma^{2}}\\\\=\sqrt{3.45}\\\\=1.85742\\\\\approx 1.86$

The standard deviation is, 1.86.

(c)

Compute the probability that the next party will be over 4 people as follows:

$P(X>4)=P(X=5)+P(X=6)+P(X=7)+P(X=8)\\\\=0.10+0.05+0.05+0.05\\\\=0.25$

Thus, the probability that the next party will be over 4 people is 0.25.

(d)

Compute the probability that the next three parties will each be over 4 people as follows:

It is provided that the three parties are independent.

P (Next 3 parties will be each over 4) = [P (X > 4)]³

$=(0.25)^{3}\\=0.015625\\\approx 0.016$

Thus, the probability that the next three parties will each be over 4 people is 0.016.

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3 years ago