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Ipatiy [6.2K]
3 years ago
11

3.11 A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If x is the nu

mber of defective sets purchased by the hotel, find the probability distribution of X. Express the results graphically as a probability histogram.

Mathematics
1 answer:
djverab [1.8K]3 years ago
7 0

Answer:

Probability distribution for x:

P(x=0)=0.3644\\\\P(x=1)=0.4373\\\\P(x=2)=0.1749\\\\P(x=3)=0.0233\\\\

Step-by-step explanation:

We can model the number of defective sets in the group of TV sets (variable x) as a binomial variable, with sample size=3 and probability of success p=2/7≈0.2857.

The probability of k defective sets in the group is:

P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}

So, we have this probabilty distribution for x:

P(x=0) = \dbinom{3}{0} p^{0}q^{3}=1*1*0.3644=0.3644\\\\\\P(x=1) = \dbinom{3}{1} p^{1}q^{2}=3*0.2857*0.5102=0.4373\\\\\\P(x=2) = \dbinom{3}{2} p^{2}q^{1}=3*0.0816*0.7143=0.1749\\\\\\P(x=3) = \dbinom{3}{3} p^{3}q^{0}=1*0.0233*1=0.0233\\\\\\

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a common what? denominator?


4 0
3 years ago
In the beginning of the study, a randomly selected group of 121 students scored an average of 252 words per minute on the readin
Alborosie

Answer:

Since the sample size is larger than 30, the cognitive psychologist can assume that the sampling distribution of M will be approximately normal.

Step-by-step explanation:

We use the central limit theorem to solve this question.

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a sample size larger than 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

So

Since the sample size is larger than 30, the cognitive psychologist can assume that the sampling distribution of M will be approximately normal.

5 0
3 years ago
Suppose a simple random sample of size nequals45 is obtained from a population with muequals64 and sigmaequals14. ​(a) What must
jeka94

Answer:

Step-by-step explanation:

Given that sample size = n=45

mu = 64 and sigma =14

a) Sample mean will follow a normal distribution irrespective of the original distributions provided

i) samples are randomly drawn

ii) samples represent the population

iii) Sample size is sufficiently large

b) Here we have sample std dev= \frac{\sigma}{\sqrt{n} } \\=\frac{14}{\sqrt{45} } \\=2.09

P(X bar>68.1) = P(Z>\frac{68.1-64}{2.09} \\=P(Z>1.96)\\=0.25

c) P(X bar>66.3) = P(Z>\frac{66.3-64}{2.09} \\=P(Z>1.10)\\=0.136

7 0
3 years ago
HELP NEED ANSWERS TO THIS QUIZ
krok68 [10]

Answer:

The answer is 14.

Step-by-step explanation:

(116-4)÷8

8 0
3 years ago
The volume of a box, a rectangular prism, is represented by the function f(x) = x3 + 7x2 + 4x – 12. The length of the box is (x
stich3 [128]

The expression represents the height of the box will be,h=(x-3).

<h3>What is volume?</h3>

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

Given data;

l= (x + 6)

w=(x + 2).

The volume of the rectangle having length l, width w, and height h is;

V=lwh

f(x)=V= x³ + 7x² + 4x – 12

lwh=x³ + 7x² + 4x – 12

Substitute the given value;

\rm (x+5)(x-1)(h)=x^3+x^2-17x+15 \\\\ (x^2+4x-5)(h)=x^3+x^2-17x+15 \\\\\ x^2+4x-5)(h)=(x2+4x-5)(x-3) \\\\ h=(x-3)

Hence, the expression represents the height of the box will be,h=(x-3).

To learn more about the volume, refer to brainly.com/question/1578538

#SPJ1

3 0
2 years ago
Read 2 more answers
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