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
To find the probability that a value lies between 36 and 48 in a normal distribution with a mean of 44 and a standard deviation of 4, we can use the Z-score formula.
The Z-score measures the number of standard deviations a given value is away from the mean. It is calculated as:
Z = (X - μ) / σ
where X is the value, μ is the mean, and σ is the standard deviation.
For the lower bound of 36:
Z = (36 - 44) / 4 = -2
For the upper bound of 48:
Z = (48 - 44) / 4 = 1
Now, we need to find the probabilities associated with these Z-scores. We can use a Z-table or a statistical calculator like Excel, Python, or an online tool.
Looking up the Z-scores in a Z-table, we find:
For a Z-score of -2, the probability is 0.0228.
For a Z-score of 1, the probability is 0.8413.
To find the probability that the value lies between 36 and 48, we subtract the probability of the lower bound from the probability of the upper bound:
0.8413 - 0.0228 = 0.8185
Therefore, the probability that a value drawn from the distribution lies between 36 and 48 is approximately 0.8185.
Since none of the given answer choices match exactly, we can round the answer to 0.82.
Therefore, the correct answer is C) 0.82.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between the two Z scores.