Answer:
25.10% probability that the spending is between 46 and 49.56 dollars
Step-by-step explanation:
Problems of normally distributed samples are 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 = 47.67, \sigma = 5.5](https://tex.z-dn.net/?f=%5Cmu%20%3D%2047.67%2C%20%5Csigma%20%3D%205.5)
What is the probability that the spending is between 46 and 49.56 dollars?
This is the pvalue of Z when X = 49.56 subtracted by the pvalue of Z when X = 46. So
X = 49.56
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{49.56 - 47.67}{5.5}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B49.56%20-%2047.67%7D%7B5.5%7D)
![Z = 0.34](https://tex.z-dn.net/?f=Z%20%3D%200.34)
has a pvalue of 0.6331
X = 46
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{46 - 47.67}{5.5}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B46%20-%2047.67%7D%7B5.5%7D)
![Z = -0.3](https://tex.z-dn.net/?f=Z%20%3D%20-0.3)
has a pvalue of 0.3821
0.6331 - 0.3821 = 0.2510
25.10% probability that the spending is between 46 and 49.56 dollars
Answer: x=6.3518
Step-by-step explanation:
Answer:
The circumference of this circle would be:
<h2>
62.831853071796</h2>
<em><u>You can round this down however you would like. Hope this helps :)</u></em>
Answer:
FV= $2,407.53
Step-by-step explanation:
Giving the following information:
Present Value (PV)= 1,300
Interest rate (i)= 4.5% = 0.045
Number of periods (n)= 14 years
<u>To calculate the future value (FV) of the initial investment after 14 years, we need to use the following formula:</u>
FV= PV*(1 + i)^n
FV= 1,300*(1.045^14)
FV= $2,407.53