MATHEMATICS COLLEGE

A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probabilities of these events:_________.A. At least one alarm is triggered.
B. More than seven alarms are triggered.
C. Eight or fewer alarms are triggered.

Answers

Answer 1

Answer:

Answer:

a) $P(X \geq 1) = 1-P(X<1) = 1-P(X=0)$

$P(X=0)=(9C0)(0.99)^0 (1-0.99)^(9-0)=1x10^(-18)$

And replacing we got:

$P(X \geq 1) =1 -1x10^(-18) \approx 1$

b) $P(X=7)=(9C7)(0.99)^7 (1-0.99)^(9-7)=0.003355$

$P(X=8)=(9C8)(0.99)^8 (1-0.99)^(9-8)=0.083047$

$P(X=9)=(9C9)(0.99)^9 (1-0.99)^(9-9)=0.913517$

And adding we got:

$P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992$

c) $P(X \leq 8) =1 -P(X>8) = 1-P(X=9)$

$P(X=9)=(9C9)(0.99)^9 (1-0.99)^(9-9)=0.913517$

And replacing we got:

$P(X \leq 8)= 1-0.913517=0.086483$

Step-by-step explanation:

Let X the random variable of interest "numebr of times that an alarm is triggered", on this case we now that:

$X \sim Binom(n=9, p=0.99)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

Part a

We want to find this probability:

$P(X \geq 1) = 1-P(X<1) = 1-P(X=0)$

$P(X=0)=(9C0)(0.99)^0 (1-0.99)^(9-0)=1x10^(-18)$

And replacing we got:

$P(X \geq 1) =1 -1x10^(-18) \approx 1$

Part b

$P(X \geq 7)= P(X=7) +P(X=8)+ P(X=9)$

$P(X=7)=(9C7)(0.99)^7 (1-0.99)^(9-7)=0.003355$

$P(X=8)=(9C8)(0.99)^8 (1-0.99)^(9-8)=0.083047$

$P(X=9)=(9C9)(0.99)^9 (1-0.99)^(9-9)=0.913517$

And adding we got:

$P(X \geq 7) = 0.003355+0.083047+0.913517 =0.99992$

Part c

$P(X \leq 8) =1 -P(X>8) = 1-P(X=9)$

$P(X=9)=(9C9)(0.99)^9 (1-0.99)^(9-9)=0.913517$

And replacing we got:

$P(X \leq 8)= 1-0.913517=0.086483$

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In the past, 21% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information. (a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09? Use a 95% confidence level. (Round your answer up to the nearest whole number.)

Answers

Answer:

A sample size of 79 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{(\pi(1-\pi))/(n)}$

In which

z is the zscore that has a pvalue of $1 - (\alpha)/(2)$ .

For this problem, we have that:

$\pi = 0.21$

The margin of error is:

$M = z\sqrt{(\pi(1-\pi))/(n)}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - (0.05)/(2) = 0.975$ , so $Z = 1.96$ .

What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

$M = z\sqrt{(\pi(1-\pi))/(n)}$

$0.09 = 1.96\sqrt{(0.21*0.79)/(n)}$

$0.09√(n) = 1.96√(0.21*0.79)$

$√(n) = (1.96√(0.21*0.79))/(0.09)$

$(√(n))^(2) = ((1.96√(0.21*0.79))/(0.09))^(2)$

$n = 78.68$

Rounding up to the nearest whole number.

A sample size of 79 is needed.

Find the constant of proportionality for the table and write in the form y = kx.A) y = 9x

B) y = 10x

C) y = 90x

D) y = 1/10x

Please give an honest answer = )

Answers

Answer:

B) y = 10x

Step-by-step explanation:

It should not be too hard for you to determine that every number on the bottom row is the same as the number on the top row with a zero appended.

Appending a zero to a number is the same as multiplying it by 10. For example, ...

... 90 = 10·9

... y = 10x

_____

In case that observation doesn't work out for you, you can always solve the given equation for k, then choose values from the table to fill in.

... y = kx

... k = y/x . . . . . divide by the coefficient of k, which is x

Fill in values from the table

... k = 20/2 = 10 . . . . . . from the second column

Now put this value where k is in the equation. After you do that, you know ...

... y = 10x

slope = (30 - 20)/(3 - 2) = 10 /1 = 10

equation

y = 10x

Answer

B) y = 10x

-4= -(x-8)
negative four equals negative (parentheses x minus 8 parentheses)

Answers

-4=-x-8
+4. +4
—————
0=-x-4
x=-4

HELP PLEASE 20points!!!At a high school, 9th and 10th graders were asked whether they would prefer
robotics or art as an elective. The results are shown in the relative frequency
table.

Answers

Answer:

61%

Step-by-step explanation:

We can see that out of all the people that were surveyed, 54% were 10th graders. Since 33% out of all the ones surveyed were 10th graders that chose robotics, the fraction would be 33/54 which is 0.611.

This is 61% approx.

Answer:

61%

Step-by-step explanation:

A P E X

Which property is illustrated by the equation –8 + 8 = 0?additive inverse
additive identity
commutative property
distributive property