Mathematics, 10.03.2020 09:03 lovelyashjoy

Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement income. In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

Answers: 2

Show answers

Answers

Answer from: hannahkharel2

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

p = 0.173, n = 120 . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 20.76}{4.14}$

Z = 3.2

Z = 3.2 has a pvalue of 0.9993

X = 21

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{21 - 20.76}{4.14}$

Z = 0.06

Z = 0.06 has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Answer from: Quest

step-by-step explanation:

Answer from: Quest

vertical asymptote $x=3$ .

horizontal asymptote $y=-1$ .

step-by-step explanation:

given function is $f\left(x\right)=\frac{-3x-5}{3x-9}$ .

vertical asymptote is given by setting

denominator =0

$3x-9=0$

$3x=9$

$x=\frac{9}{3}$

$x=3$

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.

$y=\frac{-3x}{3x}$

$y=-1$

Graph all vertical and horizontal asymptotes of the function. f(x)= -3x-5 3x-9 if anyone can it’d

Another question on Mathematics

Mathematics, 21.06.2019 19:00

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Write the summation to estimate the area under the curve y = 1 + x2 from x = -1 to x = 2 using 3 rectangles and right endpoints

Answers: 1

Answer

Mathematics, 21.06.2019 21:20

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.4 cm. use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (round your answers to four decimal places.) (a) the volume of the cube maximum possible error cm3 relative error percentage error % (b) the surface area of the cube maximum possible error cm2 relative error percentage error %

Answers: 3

Answer

Mathematics, 22.06.2019 01:30

Josie buys a pair of boots that retail for $52.00 dollars, however they are currently on sale for 25% off how much does josie pay for the boots if there is also a 6% sales tax on them

Answers: 1

Answer

You know the right answer?

Of the total population of American households, including older Americans and perhaps some not so ol...

Questions