MATHEMATICS COLLEGE

Someone plesae answer this!!

Answers

Answer 1

Answer:

Answer:

7 units is the answer

Step-by-step explanation:

points are (-9,-8) and (-2,-8)

Pythagorean theorem can written as,

$d=√((x_2-x_1)^2 + (y_2-y_1)^2) \n\nd=√((-2-(-9))^2 + (-8-(-8))^2)\n\nd=√((7\n)^2+(0)^2) \n\nd=√(49) \n\nd=7 \n\n$

∴ d = 7 units

Answer 2

Answer:

Answer:

7 units

Step-by-step explanation:

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Some parts of California are particularly earthquake- prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with proba bility (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.] b. Draw the corresponding probability histogram. c. What is the most likely value for X

Answers

Answer:

a. Binomial random variable (n=4, p=0.25)

b. Attached.

c. X=1

Step-by-step explanation:

This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).

a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:

$P(x=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\n\n\nP(x=k) = \dbinom{4}{k} 0.25^(0)\cdot0.75^(4)$

The sample space for X is {0,1,2,3,4}

The associated probabilties are:

$P(x=0) = \dbinom{4}{0} p^(0)(1-p)^(4)=1*1*0.3164=0.3164\n\n\nP(x=1) = \dbinom{4}{1} p^(1)(1-p)^(3)=4*0.25*0.4219=0.4219\n\n\nP(x=2) = \dbinom{4}{2} p^(2)(1-p)^(2)=6*0.0625*0.5625=0.2109\n\n\nP(x=3) = \dbinom{4}{3} p^(3)(1-p)^(1)=4*0.0156*0.75=0.0469\n\n\nP(x=4) = \dbinom{4}{4} p^(4)(1-p)^(0)=1*0.0039*1=0.0039\n\n\n$

b. The histogram is attached.

c. The most likely value for X is the expected value for X (E(X)).

Is calculated as:

$E(X)=np=4\cdot0.25=1$

IQ scores are normally distributed with a mean of 105 and a standard deviation of 17. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample. If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.

Answers

Answer:

Mean 105

Standard deviation 1.89

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$