### MS 150 Statistics Spring 2003 Quiz 6 • Name:

The College of Micronesia-FSM entrance test had a TOEFL mean of µ = 433 with a standard deviation of s = 79 for 1100 students. The scores were normally distributed. Find the predicted number of students who will place into the Intensive English Program (IEP) by completing the steps below. A TOEFL score between 400 and 470 will place a student into this program.

- _____ What is the mean µ?
- _____ What is the standard deviation s?
- _____ Use the formula z = to convert 400 to a z value.
- _____ Use the formula z = to convert 470 to a z value.
- Use the above values to rewrite P(400 <x < 470) as a z interval: P( ______ < z < _____)
- Sketch a normal curve with an x and z axis, placing your values calculated above on the axes.
- ________ Use the Excel function =NORMSDIST(z) and the value from number three above to calculate the area to the left of the z value for x = 400.
- ________ Use the Excel function =NORMSDIST(z) and the value from number four above to calculate the area to the left of the z value for x = 470.
- ________ Use the two answers above and your sketch to determine the area (probability) that a student will place into the IEP.
- ________ Use the probability in nine above to estimate the number of students out of the 1100 who will place into the IEP.