Question
A normal distribution has a mean of 4 and a standard deviation of 1. What percent of values are from 4 to 7?
Question content area bottom
Part 1
enter your response here% of the values are from 4 to 7.
(Type an integer or a decimal.)
Question content area bottom
Part 1
enter your response here% of the values are from 4 to 7.
(Type an integer or a decimal.)
Answers
GPT 3.5
Since the mean is 4 and the standard deviation is 1, we can calculate the z-scores for 4 and 7:
For 4:
Z = (4-4)/1 = 0
For 7:
Z = (7-4)/1 = 3
Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores.
From the table or calculator, we find that the area between 0 and 3 (representing the values from 4 to 7 in terms of standard deviations) is approximately 0.49865 or 49.865%.
Therefore, 49.865% of values are from 4 to 7 in a normal distribution with a mean of 4 and standard deviation of 1.
For 4:
Z = (4-4)/1 = 0
For 7:
Z = (7-4)/1 = 3
Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores.
From the table or calculator, we find that the area between 0 and 3 (representing the values from 4 to 7 in terms of standard deviations) is approximately 0.49865 or 49.865%.
Therefore, 49.865% of values are from 4 to 7 in a normal distribution with a mean of 4 and standard deviation of 1.