Answer: 0.670
Step-by-step explanation:
Given that :
Population mean (μ) = 11.5
Sample size, n = 22
Sample mean, x = 11.7
Standard deviation, s = 1.4
The test statistic ;
Tstat = (x - μ) / (s/√n)
Tstat = (11.7 - 11.5) / (1.4/sqrt(22))
Tstat = 0.2 / 0.2984810
Tstat = 0.6700594
Tstat = 0.670 (3 decimal places )
Answer:
144 pages read
Step-by-step explanation:
80% = 0.8
0.8 * 180 = 144
If this question is typed correctly then the answer would be 13 hours and 15 minutes
Answer:
The limit that 97.5% of the data points will be above is $912.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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.
In this problem, we have that:
![\mu = 1500, \sigma = 300](https://tex.z-dn.net/?f=%5Cmu%20%3D%201500%2C%20%5Csigma%20%3D%20300)
Find the limit that 97.5% of the data points will be above.
This is the value of X when Z has a pvalue of 1-0.975 = 0.025. So it is X when Z = -1.96.
So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-1.96 = \frac{X - 1500}{300}](https://tex.z-dn.net/?f=-1.96%20%3D%20%5Cfrac%7BX%20-%201500%7D%7B300%7D)
![X - 1500 = -1.96*300](https://tex.z-dn.net/?f=X%20-%201500%20%3D%20-1.96%2A300)
![X = 912](https://tex.z-dn.net/?f=X%20%3D%20912)
The limit that 97.5% of the data points will be above is $912.
Answer:
![y = f(x - 1) + 2](https://tex.z-dn.net/?f=y%20%3D%20f%28x%20-%201%29%20%2B%202)
Step-by-step explanation:
Let's say that the dotted graph is y.
See f(3) = 0 or (3,0). Let's call that the point of interest. Notice that our point of interest has to move to the right by 1 unit to get to the dotted graph. so
![y = f(x - 1)](https://tex.z-dn.net/?f=y%20%3D%20f%28x%20-%201%29)
And it has to go up by two units so
![y = f(x - 2) + 2](https://tex.z-dn.net/?f=y%20%3D%20f%28x%20-%202%29%20%2B%202)