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ludmilkaskok [199]
3 years ago
12

If a seed is planted, it has a 90% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that

exactly 2 don't grow
Mathematics
1 answer:
blondinia [14]3 years ago
5 0

Answer:

0.2301 = 23.01% probability that exactly 2 don't grow.

Step-by-step explanation:

For each seed planted, there are only two possible outcomes. Either it grows into a healthy plant, or it does not. The probability of a seed growing into a healthy plant is independent of any other seed, which means that the binomial probability distribution is used 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.

90% chance of growing into a healthy plant.

This means that p = 0.9

12 seeds are planted

This means that n = 12

What is the probability that exactly 2 don't grow?

So 12 - 2 = 10 grow, which is P(X = 10). Then

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

P(X = 10) = C_{12,10}.(0.9)^{10}.(0.1)^{2} = 0.2301

0.2301 = 23.01% probability that exactly 2 don't grow.

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Answer:

Step-by-step explanation:

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GarryVolchara [31]

Answer:

\mu_p -\sigma_p = 0.74-0.0219=0.718

\mu_p +\sigma_p = 0.74+0.0219=0.762

68% of the rates are expected to be betwen 0.718 and 0.762

\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696

\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784

95% of the rates are expected to be betwen 0.696 and 0.784

\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674

\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806

99.7% of the rates are expected to be betwen 0.674 and 0.806

Step-by-step explanation:

Check for conditions

For this case in order to use the normal distribution for this case or the 68-95-99.7% rule we need to satisfy 3 conditions:

a) Independence : we assume that the random sample of 400 students each student is independent from the other.

b) 10% condition: We assume that the sample size on this case 400 is less than 10% of the real population size.

c) np= 400*0.74= 296>10

n(1-p) = 400*(1-0.74)=104>10

So then we have all the conditions satisfied.

Solution to the problem

For this case we know that the distribution for the population proportion is given by:

p \sim N(p, \sqrt{\frac{p(1-p)}{n}})

So then:

\mu_p = 0.74

\sigma_p =\sqrt{\frac{0.74(1-0.74)}{400}}=0.0219

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

\mu_p -\sigma_p = 0.74-0.0219=0.718

\mu_p +\sigma_p = 0.74+0.0219=0.762

68% of the rates are expected to be betwen 0.718 and 0.762

\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696

\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784

95% of the rates are expected to be betwen 0.696 and 0.784

\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674

\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806

99.7% of the rates are expected to be betwen 0.674 and 0.806

5 0
3 years ago
A furniture store is having a sale on sofas and you're going to buy one. The advertisers know that buyers get to the store and t
MrRissso [65]

Answer:

$290

Step-by-step explanation:

We are told that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement.

Now we are told that the advertised sofa is $250 and the more expensive sofa is $450.

Thus;

P(x) for expensive sofa = 1/5

P(x) for sofa in sale advertisement = 4/5

Thus, expected value is;

E(X) = (1/5)450 + (4/5)250

E(x) = 90 + 200

E(x) = $290

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PLEASE HELP!!!! Choose the best graph that represents the linear equation: 4x + y = 0 Graph A On a coordinate plane, a line goes
arlik [135]

Answer:

see graph...

B On a coordinate plane, a line goes through (0, 0) and (1, negative 4).

Step-by-step explanation:

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You recently invested $400,000 of your savings in a security issued by a large company. The security agreement pays you 12% per
ANTONII [103]

Answer:

$722444.49386776

Step-by-step explanation:

Use Compound Intrest Formula

a = p(1 +  \frac{r}{n} ) {}^{nt}

  • where p is the original amount.
  • R is the amount of percentage compounded
  • N is amount of times compounded per year.
  • T is how long the interest last.

P is 400,00p

T is 12% or 0.12

N is 4 since it is compounded quarterly

T is 5.

Plug the values in

400000(1 +  \frac{0.12}{4} ) {}^{20}

Ypu get

$722444.49386776

6 0
3 years ago
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