Answer:
So we can find this probability:
![P(-1.778](https://tex.z-dn.net/?f=%20P%28-1.778%3CZ%3C1.778%29%20%3D%20P%28Z%3C1.778%29%20-P%28Z%3C-1.778%29%20%3D0.962-0.0377%3D%200.9243)
And then since the interest is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches using the complement rule we got:
![P = 1-0.9243 = 0.0757](https://tex.z-dn.net/?f=%20P%20%3D%201-0.9243%20%3D%200.0757)
Step-by-step explanation:
Let X the random variable that represent the diamters of interest for this case, and for this case we know the following info
Where
and
We can begin finding this probability this probability
For this case they select a sample of n=79>30, so then we have enough evidence to use the central limit theorem and the distirbution for the sample mean can be approximated with:
![\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Csim%20N%28%5Cmu%2C%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%29)
And the best way to solve this problem is using the normal standard distribution and the z score given by:
And we can find the z scores for each limit and we got:
So we can find this probability:
![P(-1.778](https://tex.z-dn.net/?f=%20P%28-1.778%3CZ%3C1.778%29%20%3D%20P%28Z%3C1.778%29%20-P%28Z%3C-1.778%29%20%3D0.962-0.0377%3D%200.9243)
And then since the interest is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches using the complement rule we got:
![P = 1-0.9243 = 0.0757](https://tex.z-dn.net/?f=%20P%20%3D%201-0.9243%20%3D%200.0757)
The remaining money will be $1062.50 after they pay for rent and give each student a $3.50 gift.
And divide that by 225(number of students) and you get 4.73$ on food
2000 to spend
$2000=$150(Park) = 1850
$1850-$787.50= $1,062.50
Answer: C. Exponential Decay function
Step-by-step explanation:
We know that In exponential decay, the total value decreases but the ratio of decreasing remains constant over time.
Here the amount in the bank account is decreasing by constant ratio of 1/2, and the amount that decreases is proportional to the money in the account, therefore, it is called exponential decay.
Hence, the given function is an exponential decay function.