Question
Which of the following percentages accurately estimates the area under a normal curve to the left of a z-score of 3.01?(1 point)
Responses
99.87 percent
99.87 percent
0.13 percent
0.13 percent
0.0013 percent
0.0013 percent
0.9987 percent
Responses
99.87 percent
99.87 percent
0.13 percent
0.13 percent
0.0013 percent
0.0013 percent
0.9987 percent
Answers
GPT-4o mini
To find the area under a normal curve to the left of a z-score of 3.01, we can refer to a standard normal distribution table or use a calculator that provides the cumulative distribution function (CDF) for the normal distribution.
A z-score of 3.01 is quite far in the tail of the distribution, and the area to the left of this z-score will be very close to 1.
Typically, the area to the left of a z-score of 3.00 is approximately 0.9987 or 99.87%. Given that 3.01 is even slightly higher, the area will be slightly more than 99.87%.
The most accurate option for a z-score of 3.01 among the choices provided is:
**0.9987 percent** or 99.87% (written as a decimal, it's 0.9987, but when considering percentages, it should be 99.87%).
So, the answer is **99.87 percent**.
A z-score of 3.01 is quite far in the tail of the distribution, and the area to the left of this z-score will be very close to 1.
Typically, the area to the left of a z-score of 3.00 is approximately 0.9987 or 99.87%. Given that 3.01 is even slightly higher, the area will be slightly more than 99.87%.
The most accurate option for a z-score of 3.01 among the choices provided is:
**0.9987 percent** or 99.87% (written as a decimal, it's 0.9987, but when considering percentages, it should be 99.87%).
So, the answer is **99.87 percent**.