Answer:


![Interval = [666.78, 781.62]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B666.78%2C%20781.62%5D)
Step-by-step explanation:
Given
The data for 25 undergraduates
Solving (a): Range and Standard deviation
The range is:

From the dataset:


So:



The standard deviation is:

First, calculate the mean



So, the standard deviation is:




Solving (b): The interval of the 95% of the observation.
Using the emperical rule, we have:
![Interval = [\bar x - 2*\sigma, \bar x+ 2*\sigma]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B%5Cbar%20x%20-%202%2A%5Csigma%2C%20%5Cbar%20x%2B%202%2A%5Csigma%5D)
![Interval = [724.2 - 2*28.71, 724.2 + 2*28.71]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B724.2%20-%202%2A28.71%2C%20724.2%20%2B%202%2A28.71%5D)
![Interval = [666.78, 781.62]](https://tex.z-dn.net/?f=Interval%20%3D%20%5B666.78%2C%20781.62%5D)
Answer:
Step-by-step explanation:
PLEASE MARK BRAINLIEST
We use the formula:
x± s <span>t_<span>(1−c)/2 / </span></span>√n = 5
(1 - c)/2 = (1 - 0.95) / 2 = 0.025
Using the t score calculator at this value, at the 95% confidence internval,
t = 0.5080, So
100 - 19(0.5080) / √n = 5
Solving for n
n = 97
a) 97
b) yes