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 80 and higher.
A)5.00
B)12.50
C)2.80
D)22.21

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 80 and higher.
A)5.00 
B)12.50 
C)2.80 
D)22.21

Quizplus · Accepted Answer

To test whether the measurements came from a normal population, we can use a chi-square goodness of fit test. 
First, we divide the data into intervals, and calculate the expected frequencies for each interval assuming a normal distribution. 
For the interval 80 and higher, we can use the formula: 
expected frequency = (total sample size) * (area to the right of 80)
To find the area to the right of 80, we need to standardize the value using the formula: 
z = (x - mean) / standard deviation
z = (80 - 50.2) / 18.7
z = 1.59
Using a standard normal distribution table or calculator, we can find that the area to the right of 1.59 is 0.057. 
Therefore, the expected frequency for the interval 80 and higher is: 
expected frequency = 50 * 0.057 = 2.85
Rounding to two decimal places, the answer is 2.80, which is option C.

Consider a Set of 50 Measurements with Mean 50