Mathematics, 07.06.2020 05:01 HappyBeatrice1401

Recent survey data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. Their parents must have a basement! A random sample of 125 young adults in this age group was selected. What is the probability that between 13 and 17 of these young adults lived with their parents? Hint: use 14.2% to determine the standard error and the p-bar would be the 13/125 and the 17/125.

Answers: 3

Show answers

Answers

Answer from: tylorroundy

38.76% probability that between 13 and 17 of these young adults lived with their parents

Step-by-step explanation:

I am going to use the normal approxiation to the binomial 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 = 0.142, n = 125

$\mu = E(X) = np = 125*0.142 = 17.75$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{125*0.142*0.858} = 3.9025$

What is the probability that between 13 and 17 of these young adults lived with their parents?

Using continuity correction, this is $P(13 - 0.5 \leq X \leq 17 + 0.5) = P(12.5 \leq 17.5)$ , which is the pvalue of Z when X = 17.5 subtracted by the pvalue of Z when X = 12.5. So

X = 17.5

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

$Z = \frac{17.5 - 17.75}{3.9025}$

Z = -0.06

Z = -0.06 has a pvalue of 0.4761

X = 12.5

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

$Z = \frac{12.5 - 17.75}{3.9025}$

Z = -1.35

Z = -1.35 has a pvalue of 0.0885

0.4761 - 0.0885 = 0.3876

38.76% probability that between 13 and 17 of these young adults lived with their parents

Answer from: Quest

why do wages differ across industries

step-by-step explanation :

micro economists are concerned with economics on an industry or individual firm basis.

macro economists are concerned with national and international level

Answer from: Quest

the answer is b

Another question on Mathematics

Mathematics, 21.06.2019 13:40

What is f(3) for the quadratic function f(x)= 2x^2+ + x - 12

Answers: 1

Answer

Mathematics, 21.06.2019 13:50

Astudent received the following grades last semester. find the student's semester grade point average. an a is algebra (3 credits), a b in history ( 3 credits), a in sociology ( 3 credits) a d in english ( 3credits) and a c in seminar ( 2credits). an a is worth 4 points, a b is worth 3 points a c is worth 2 points and a d is worth 1 point.

Answers: 2

Answer

Mathematics, 21.06.2019 18:00

Sandy is ordering bread rolls for her party,she wants 3/5 of the rolls to be whole wheat. what other factions can represent part of the rolls that will be whole wheat? shade the models to show your work.

Answers: 1

Answer

Mathematics, 22.06.2019 02:30

Joyce deposited $5000 in an account with an annual interest rate of 6%, compounded annually. how much money will be in the account 10 years later

Answers: 2

Answer

You know the right answer?

Recent survey data indicated that 14.2% of adults between the ages of 25 and 34 live with their pare...

Questions

Mathematics, 02.06.2020 19:58

The top of a bench has a length of 15 ft and a width of 9 ft. A second bench is similar to the first bench. The top of the second bench is 10 ft long....