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marusya05 [52]
2 years ago
8

According to an​ almanac, 60​% of adult smokers started smoking before turning 18 years old. ​(a) compute the mean and standard

deviation of the random variable​ x, the number of smokers who started before 18 in 400 trials of the probability experiment. ​(b) interpret the mean. ​(c) would it be unusual to observe 340 smokers who started smoking before turning 18 years old in a random sample of 400 adult​ smokers? why?
Mathematics
1 answer:
larisa [96]2 years ago
5 0
The given problem describes a binomial distribution with p = 60% = 0.6. Given that there are 400 trials, i.e. n = 400.

a.) The mean is given by:

\mu=np=400\times0.6=240

The standard deviation is given by:

\sigma=\sqrt{npq} \\  \\ =\sqrt{np(1-p)} \\  \\ =\sqrt{400(0.6)(0.4)} \\  \\ =\sqrt{96}=9.80


b.)  The mean means that in an experiment of 400 adult smokers, we expect on the average to get about 240 smokers who started smoking before turning 18 years.


c.) It would be unusual to observe <span>340 smokers who started smoking before turning 18 years old in a random sample of 400 adult​ smokers because 340 is far greater than the mean of the distribution.
340 is greater than 3 standard deviations from the mean of the distribution.</span>
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Translate this sentence into an equation.: Mai's savings increased by 15 is 65. Use the variable m to represent Mai's savings.
Schach [20]
M+15=65 could this be the answer you are possibly looking for? if the m is Mai's savings "increased by 15" would simply be adding 15 and it would be equal to 65
7 0
3 years ago
The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure
Ilia_Sergeevich [38]

Answer:

a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

Step-by-step explanation:

For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?

The foreclosure rate is 1.31% for the Washington, DC area, which means that p = 0.0131

We wanto to find, with n = 100:

P(X < 2) = P(X = 0) + P(X = 1)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0131)^{0}.(0.9869)^{100} = 0.2675

P(X = 1) = C_{100,1}.(0.0131)^{1}.(0.9869)^{99} = 0.3551

P(X < 2) = P(X = 0) + P(X = 1) = 0.2675 + 0.3551 = 0.6226

0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?

Foreclosure rate of 0.87% for the nation, which means that p = 0.0087. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0087)^{0}.(0.9913)^{100} = 0.4174

P(X = 1) = C_{100,1}.(0.0087)^{1}.(0.9913)^{99} = 0.3663

P(X < 2) = P(X = 0) + P(X = 1) = 0.4174 + 0.3663 = 0.7837

0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c. Comment on the above findings.

The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

7 0
3 years ago
Which expression represents the slope of a line that passes through the points (0, 0) and (x, y)
yaroslaw [1]

Answer:

Yuhh the answers c dawhggg trus me i just did the same thing lawl!

Step-by-step explanation:

6 0
3 years ago
100 yards on 20 carries
Svetlanka [38]

Answer:

if u multiply 20 times 5 u would get 100 and and if u add 20+20+20+20+20 u would get 100 so either way ur answer may be 5

4 0
2 years ago
Help........................
MrRissso [65]

since the powers are same, ignore 'em , and let's calculate the bases.

-16.(1/2)

-8.1 (upon cancellation)

ans = -8

hope it helps...!!!

5 0
2 years ago
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