The time required to finish a test in normally distributed with a mean of 40 minutes and a standard deviation of 8 minutes. What is the probability that a student chosen at random will finish the test between 24 and 48 minutes?
82%
2%
84%
16%
enter your numbers on this web page and you can see that the answer is 82%
http://davidmlane.com/hyperstat/z_table.html
If you play around with things a bit, it should make things clearer.
To find the probability that a student will finish the test between 24 and 48 minutes, we need to calculate the area under the normal distribution curve between these two values.
The first step is to standardize the values of 24 and 48. We can do this by subtracting the mean (40 minutes) from each value and then dividing by the standard deviation (8 minutes):
Standardized value for 24 minutes = (24 - 40) / 8 = -2
Standardized value for 48 minutes = (48 - 40) / 8 = 1
Next, we need to find the area under the normal distribution curve from -2 to 1. This can be done using a standard normal distribution table or by using a calculator or software that can calculate normal distribution probabilities.
Using a standard normal distribution table, we can find the probabilities associated with the standardized values:
Φ(-2) = 0.0228 (probability associated with -2)
Φ(1) = 0.8413 (probability associated with 1)
To find the probability between -2 and 1, we subtract the probability associated with -2 from the probability associated with 1:
0.8413 - 0.0228 = 0.8185
Therefore, the probability that a student chosen at random will finish the test between 24 and 48 minutes is approximately 0.8185, or 82%.
So the correct answer is 82%.