Answer:
$43
Step-by-step explanation:
She overdrew her account means she has a negative balance of $7
Old balance: -7
She adds $50
New Balance: $50 - $7 = $43
Answer:
It would be an improper fraction a = ![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
Step-by-step explanation:
An improper fraction is when a fraction in which the numerator is greater than the denominator.
Answer:
a
The 95% confidence interval is ![0.0503 < p < 0.1297](https://tex.z-dn.net/?f=0.0503%20%20%3C%20%20%20p%20%3C%200.1297)
b
The sample proportion is ![\r p = 0.09](https://tex.z-dn.net/?f=%5Cr%20p%20%3D%20%200.09)
c
The critical value is ![Z_{\frac{\alpha }{2} } = 1.96](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3D%20%201.96)
d
The standard error is ![SE =0.020](https://tex.z-dn.net/?f=SE%20%20%20%3D0.020)
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is ![H_o : p = 0.08](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20p%20%20%3D%20%200.08)
The alternative hypothesis is ![H_a : p > 0.08](https://tex.z-dn.net/?f=H_a%20%20%3A%20%20p%20%3E%200.08)
Generally the sample proportion is mathematically evaluated as
![\r p = 0.09](https://tex.z-dn.net/?f=%5Cr%20p%20%3D%20%200.09)
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
![\alpha = 100 - 95](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%20100%20-%20%2095)
![\alpha = 5\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%205%5C%25)
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.05)
Next we obtain the critical value of
from the normal distribution table, the value is
![Z_{\frac{\alpha }{2} } = 1.96](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3D%20%201.96)
Generally the standard of error is mathematically represented as
![SE = \sqrt{\frac{\r p (1 - \r p)}{n} }](https://tex.z-dn.net/?f=SE%20%20%20%3D%20%20%5Csqrt%7B%5Cfrac%7B%5Cr%20p%20%281%20-%20%20%5Cr%20p%29%7D%7Bn%7D%20%7D)
substituting values
![SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }](https://tex.z-dn.net/?f=SE%20%20%20%3D%20%20%5Csqrt%7B%5Cfrac%7B0.09%20%20%281%20-%20%200.09%29%7D%7B200%7D%20%7D)
![SE =0.020](https://tex.z-dn.net/?f=SE%20%20%20%3D0.020)
The margin of error is
![E = Z_{\frac{ \alpha }{2} } * SE](https://tex.z-dn.net/?f=E%20%3D%20%20Z_%7B%5Cfrac%7B%20%5Calpha%20%7D%7B2%7D%20%7D%20%20%2A%20SE)
=> ![E = 1.96 * 0.020](https://tex.z-dn.net/?f=E%20%3D%20%201.96%20%20%2A%20%200.020)
=> ![E = 0.0397](https://tex.z-dn.net/?f=E%20%3D%20%200.0397)
The 95% confidence interval is mathematically represented as
![\r p - E < \mu < p < \r p + E](https://tex.z-dn.net/?f=%5Cr%20p%20%20-%20%20E%20%20%3C%20%20%5Cmu%20%3C%20%20p%20%3C%20%20%5Cr%20p%20%20%2B%20E)
=> ![0.09 - 0.0397 < \mu < p < 0.09 + 0.0397](https://tex.z-dn.net/?f=0.09%20-%200.0397%20%20%3C%20%20%5Cmu%20%3C%20%20p%20%3C%200.09%20%2B%200.0397)
=> ![0.0503 < p < 0.1297](https://tex.z-dn.net/?f=0.0503%20%20%3C%20%20%20p%20%3C%200.1297)
The figure below shows the standard normal distribution or "bell-shaped" curve, plotted against the z-score.
The z-score is defined as
z = (x - μ)/σ
where
x = nrandom variable
μ = mean
σ = standard deviation.
As z-values decrease, areas to the left of z decrease as shown by the shaded area.
Answer:
Areas to the left of z decrease.