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3 years ago

Solve 1 expression Please do everything in great detail (well, just a very great detail)

Mathematics

1 answer:

monitta3 years ago

5 0

Remember the distributive property
a(b+c)=ab+ac

so
first distribute
(2/3a-0.8)(a-0.8)=0.64
focus on the left side

(2/3a-0.8)(a-0.8)=
(a)(2/3a-0.8)+(-0.8)(2/3a-0.8)=
(2/3a^2)+(-0.8a)+(-1.6/3a)+(0.64)=
2/3a^2-4/3a+0.64
now we do
2/3a^2-4/3a+0.64=0.64
minus 0.64 both sides
2/3a^2-4/3a=0
factor
(a)(2/3a-4/3)=0
set each to zero
a=0

2/3a-4/3=0
add 4/3 both sides
2/3a=4/3
times 3 bohth sides
2a=4
divide 2
a=2

a=0 or 2

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lower limit =0.261

upper limit =0.369

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A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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Description in words of the parameter p

$p$ represent the real population proportion of people that have experienced bullying

X= 63 people in the random sample that have experienced bullying

n=200 is the sample size required

$\hat p=\frac{63}{200}=0.315$ represent the estimated proportion of people that have experienced bullying

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

$\hat p=\frac{63}{200}=0.315$ represent the estimated proportion of people that they were planning to pursue a graduate degree

Confidence interval

The confidence interval for a proportion is given by this formula

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For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.