Question
A normal distribution has a mean of 4 and a standard deviation of 1. What percent of values are from 4 to 5? Question content area bottom Part 1 enter your response here% of the values are from 4 to 5. (Type an integer or a decimal.
Answers
GPT 3.5
To find the percentage of values between 4 and 5 in a normal distribution with a mean of 4 and a standard deviation of 1, we can use the properties of the standard normal distribution.
First, we need to convert the values of 4 and 5 into z-scores using the formula:
z = (x - mean) / standard deviation
For x = 4:
z = (4 - 4) / 1 = 0
For x = 5:
z = (5 - 4) / 1 = 1
Next, we can look up the corresponding z-scores in a standard normal distribution table or use a calculator to find the percentage of values between z = 0 and z = 1. This area corresponds to the percentage of values between 4 and 5 in the normal distribution.
Using a standard normal distribution table or calculator, we find that the percentage of values between 0 and 1 in a standard normal distribution is approximately 34.13%.
Therefore, approximately 34.13% of values are between 4 and 5 in the normal distribution with mean 4 and standard deviation 1.
First, we need to convert the values of 4 and 5 into z-scores using the formula:
z = (x - mean) / standard deviation
For x = 4:
z = (4 - 4) / 1 = 0
For x = 5:
z = (5 - 4) / 1 = 1
Next, we can look up the corresponding z-scores in a standard normal distribution table or use a calculator to find the percentage of values between z = 0 and z = 1. This area corresponds to the percentage of values between 4 and 5 in the normal distribution.
Using a standard normal distribution table or calculator, we find that the percentage of values between 0 and 1 in a standard normal distribution is approximately 34.13%.
Therefore, approximately 34.13% of values are between 4 and 5 in the normal distribution with mean 4 and standard deviation 1.