Converting Measurements between Systems

Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

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

6 0

4 years ago

Zachary can spend no more than $94 per day to rent a car. A car rents for $30 per day plus $0.20 per mile. Write an inequality f

Temka [501]

Answer:

$124.20 miles all you gotta do is add them together

Step-by-step explanation:

5 0

3 years ago

Enlarge the triangle by scale factor 0.5 using 3,1 as the centre of enlargement

NISA [10]

Answer:

the points are :

(0,-1)

(0,0)

(-1,3)

(If you are using MathsWatch) For this question the triangle gets smaller so i'm not sure why it says Enlarge the triangle.

6 0

3 years ago

A cable runs from the top of a pole to a spot on the ground 10 feet from the base of the pole. The pole makes a right angle with

Amanda [17]

Use the cos ratio to figure this out. You have the length of the hypotenuse and the length of the leg on the ground. The hypotenuse is 20 and the leg is 10. The cos ratio says that cosA = side adjacent/hypotenuse. So fill in the blanks here: cosA = 10/20...cosA=1/2. In your calculator, you will enter inverse cos(.5) to find that the angle in question is 60 degrees. To find the inverse function on your calculator, press the "2nd" button and the "cos" then in the (), enter ".5".

7 0

3 years ago

Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkboo

Inessa [10]

Eliza started out with $324.18 on Jan. 18th and had outstanding cheques of $15.00+77.49+$124.28=$216.77. So her actual balance was $324.18-$216.77=$107.41. Now she has $487.38 so $487.38-$107.41=$379.97 balance for the deposited amount.

4 0

3 years ago