A normal distribution has a mean of 44 and a standard deviation of 4.
What is the probability that a value drawn from the distribution lies between 36 and 48?
A)
0.18
B)
0.32
C)
0.82
D)
0.91
Enter your numbers here
http://davidmlane.com/hyperstat/z_table.html
to get a feel for how this stuff works.
To find the probability that a value drawn from the distribution lies between 36 and 48, we need to calculate the area under the normal curve within this range.
First, we need to standardize the values of 36 and 48 using the formula:
Z = (X - μ) / σ
Where:
- X is the value we want to standardize (36 and 48 in this case)
- μ is the mean of the distribution (44 in this case)
- σ is the standard deviation of the distribution (4 in this case)
For 36:
Z = (36 - 44) / 4 = -2
For 48:
Z = (48 - 44) / 4 = 1
Next, we can use a standard normal distribution table or a calculator to find the area under the curve between -2 and 1. This represents the probability that a value drawn from the distribution lies between 36 and 48.
Looking up the values in the standard normal distribution table, we find that the area to the left of -2 is approximately 0.0228, and the area to the left of 1 is approximately 0.8413.
To find the area between -2 and 1, we subtract the smaller area from the larger area:
Area between -2 and 1 = 0.8413 - 0.0228 = 0.8185
Therefore, the probability that a value drawn from the distribution lies between 36 and 48 is 0.8185.
Since none of the given options match this probability exactly, it seems that there might be a mistake in the answer choices provided.