The confidence interval is
![0.58\pm0.04](https://tex.z-dn.net/?f=0.58%5Cpm0.04)
.
This means that if we take repeated samples, 99% of the intervals would contain the population proportion.
To construct this interval, we use
![p\pm z*\sigma_p](https://tex.z-dn.net/?f=p%5Cpm%20z%2A%5Csigma_p)
,
where
![sigma_p=\sqrt{\frac{p(1-p)}{N}}](https://tex.z-dn.net/?f=sigma_p%3D%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7BN%7D%7D)
Since 590/1016 said they had a cat and a dog, p=0.581 and N=1016:
![\sigma_p=\sqrt{\frac{0.581(1-0.581)}{1016}}=\sqrt{\frac{0.581(0.419)}{1016}}=0.015.](https://tex.z-dn.net/?f=%5Csigma_p%3D%5Csqrt%7B%5Cfrac%7B0.581%281-0.581%29%7D%7B1016%7D%7D%3D%5Csqrt%7B%5Cfrac%7B0.581%280.419%29%7D%7B1016%7D%7D%3D0.015.)
We need the z-score associated with this confidence level:
Convert 99% to a decimal: 99/100 = 0.99
Subtract from 1: 1-0.95 = 0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995
Using a z-table, we see that this value is equally distant from z=2.57 and z=2.58, so we will use z=2.575:
Answer:
Step-by-step explanation:
You can't solve for the values of a and b because 6a³b²·2a⁴b³ is an expression, not an equation. However, you can simplify the expression:
6a³b²·2a⁴b³ = 6·2·a³⁺⁴b²⁺³ = 12a⁷b⁵
It will take her 16 months to save $180.
Answer:
a = 14, b = 2
Step-by-step explanation:
the initial amount was 14
the growth factor is 2