Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies. It is desired to test whether these measurements came from a normal population. Calculate the expected frequency for the interval 0-39.99.
A)10.44
B)12.00
C)14.56
D)12.50

Question

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies.  It is desired to test whether these measurements came from a normal population. Calculate the expected frequency for the interval 0-39.99.
A)10.44 
B)12.00 
C)14.56 
D)12.50

Quizplus · Accepted Answer

To test if the measurements came from a normal population, we need to use the normal distribution. We can estimate the expected frequency for the interval 0-39.99 by finding the area under the normal curve for this interval, using the mean and standard deviation of the data set. 
Using a z-score table, we can find the z-score for the lower bound of this interval as follows: 
z = (39.99 - 50.2) / 18.7 = -0.55
The area under the normal curve for this interval is equal to the area to the left of this z-score, which is 0.2912.
Therefore, the expected frequency for this interval is:
Expected frequency = 50 * 0.2912 = 14.56
So, the best choice is C.

Consider a Set of 50 Measurements with Mean 50