Answer:
The probability is ![P(X \le 0.305 ) = 0.01795](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%20%200.01795)
Step-by-step explanation:
From the question we are told that
The population mean is ![\mu = 0.966 \ grams](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%200.966%20%5C%20grams)
The standard deviation is ![\sigma = 0.315 \ grams](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%200.315%20%5C%20%20grams)
Given that the amounts of nicotine in a certain brand of cigarette are normally distributed
Then the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less is mathematically represented as
![P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(\frac{X - \mu }{\sigma } > \frac{0.305 - \mu }{\sigma } )](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%20%201%20-%20%20P%28%5Cfrac%7BX%20-%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%3E%20%5Cfrac%7B0.305%20-%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%20%29)
Generally
![\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of X )](https://tex.z-dn.net/?f=%5Cfrac%7BX%20-%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%3D%20%20Z%20%20%28The%20%20%5C%20standardized%20%5C%20%20value%20%20%5C%20%20of%20%20X%20%29)
So
![P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z > \frac{0.305 - 0.966 }{0.315} )](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%20%201%20-%20%20P%28Z%20%3E%20%5Cfrac%7B0.305%20-%200.966%20%7D%7B0.315%7D%20%20%20%29)
![P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z >-2.0984 )](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%20%201%20-%20%20P%28Z%20%3E-2.0984%20%29)
From the z-table(reference calculator dot net ) value of ![P(Z >-2.0984 ) =0.98205](https://tex.z-dn.net/?f=P%28Z%20%3E-2.0984%20%29%20%3D0.98205)
So
![P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - 0.98205](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%20%201%20-%20%200.98205)
=> ![P(X \le 0.305 ) = 1 - P(X > 0.305) = 0.01795](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%201%20-%20P%28X%20%3E%20%200.305%29%20%3D%200.01795)
=> ![P(X \le 0.305 ) = 0.01795](https://tex.z-dn.net/?f=P%28X%20%5Cle%200.305%20%29%20%3D%20%20%200.01795)
Answer:
2160 square units
Step-by-step explanation:
Given data
Radius= 6 units
Angle= 120°
Area of the sector is given as
Area of sector= r^2* ∅/2
Area of sector= 6^2*120/2
Area of sector= 36*60
Area of sector= 2160 square units
Answer:
Monday and tuesday!
Step-by-step explanation:
The reason why this is your answer is that they are even colder than 1.75 celsius.
Thanks!
Mark me brainliest!
Answer:
it has one solution
Step-by-step explanation: