A sample of 500 evening students revealed that their annual incomes were normally distributed with a mean income of $50,000 and a standard deviation of $4,000. How many students earned between $45,000 and $53,000?
A) 170
B) 273
C) 334
D) 387

Question

Quizplus · Accepted Answer

To find the number of students who earned between $45,000 and $53,000, we need to find the z-scores for each of these values and use them in the standard normal distribution table.

z-score for $45,000: 
z = (45,000 - 50,000) / 4,000 
z = -1.25

z-score for $53,000: 
z = (53,000 - 50,000) / 4,000 
z = 0.75

Using the standard normal distribution table, we can find the area between these two z-scores:

Area between z = -1.25 and z = 0.75 
= 0.7734 - 0.1056 
= 0.6678

To find the number of students, we need to multiply this area by the total number of students:

0.6678 x 500 = 334

Therefore, the answer is C.

A Sample of 500 Evening Students Revealed That Their Annual