The mean time to complete a psychology exam is 34 minutes with a standard deviation of 8 minutes. Assume the distribution is normal. Find the probability of a student taking less than 28 minutes.
Z=(28-μ)/σ
Look up the standard normal distribution table and look at the percentage for the left tail.
To find the probability of a student taking less than 28 minutes to complete the psychology exam, we can use the concept of standard deviation and the properties of the normal distribution.
Step 1: Standardize the value
To calculate the probability, we need to standardize the value of 28 minutes using the formula:
z = (x - μ) / σ
where
- z is the standardized value,
- x is the given value (28 minutes in our case),
- μ is the mean (34 minutes),
- σ is the standard deviation (8 minutes).
Plugging in the values, we get:
z = (28 - 34) / 8 = -0.75
Step 2: Look up the z-score
Next, we need to look up the z-score in the standard normal distribution table. This table provides the area under the normal curve for different z-scores.
Looking up the z-score of -0.75 in the standard normal distribution table, we find that it corresponds to approximately 0.2266.
Step 3: Calculate the probability
Since we want to find the probability of a student taking less than 28 minutes, we need to find the area to the left of the given z-score. This can be done by subtracting the area (probability) from 0.5 (as the total probability under the curve is 1).
P(x < 28) = 0.5 - 0.2266 = 0.2734
So, the probability of a student taking less than 28 minutes to complete the psychology exam is approximately 0.2734 or 27.34%.