Answer: 139
Step-by-step explanation:
As per given , we have
The amount of caffeine per cup is ranging from 60-180 mg.
Range = Maximum - Minimum = 180 -60 =12
According to Range -rule ,
Standard deviation = ![s\approx\dfrac{Range}{4}=\dfrac{120}{4}=30](https://tex.z-dn.net/?f=s%5Capprox%5Cdfrac%7BRange%7D%7B4%7D%3D%5Cdfrac%7B120%7D%7B4%7D%3D30)
Formula for sample size :
, where z* is critical z value and E is margin of error.
By z-table , the critical z-value for 95% confidence interval = 1.96
E= 5
Put all values in formula , we get
![n=(\dfrac{(1.96)\times 30}{5})^2=138.2976\approx139](https://tex.z-dn.net/?f=n%3D%28%5Cdfrac%7B%281.96%29%5Ctimes%2030%7D%7B5%7D%29%5E2%3D138.2976%5Capprox139)
Hence, 139 cups of coffee would have be included in the sample.