Let f(x) = 4x − 3. If f(a) = 9 and f(b) = 5, then what is f(a + b) ?

1 answer:

7 0

F(x) = 4x - 3

f(a) = 4a-3

9 = 4a-3

4a = 12

a = 12 / 4

a = 3

_____________________

f(b) = 4b-3

5+3 = 4b

8 = 4b

b = 8 / 4

b = 2

___________________

f(a+b) = 4(a+b) - 3

f(a+b) = 4(3+2) - 3

f(a+b) = 4(5) - 3

f(a+b) = 20 - 3

f(a+b) = 17

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Answer:

a) The 99% confidence interval would be given (0.523;0.577).

We are 99% confident that this interval contains the true population proportion.

b) $n=\frac{0.55(1-0.55)}{(\frac{0.03}{2.58})^2}=1830.51$

And rounded up we have that n=1831

Step-by-step explanation:

Data given and notation

n=2341 represent the random sample taken

X represent the people that they have watched digitally streamed TV programming on some type of device

$\hat p=0.55$ estimated proportion of people that they have watched digitally streamed TV programming on some type of device

$\alpha=0.01$ represent the significance level

Confidence =0.99 or 99%

z would represent the statistic for the confidence interval

p= population proportion of people that they have watched digitally streamed TV programming on some type of device

The population proportion present the following distribution:

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

Part a) Confidence interval

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.