SOLUTION: Can a tutor so kindly review these problems and show me how to do them step by step? Suppose the scores of certain standardized test are normally distributed with mean 500 and s

Click here to see ALL problems on Probability-and-statistics

Question 469011: Can a tutor so kindly review these problems and show me how to do them step by step?
Suppose the scores of certain standardized test are normally distributed with mean 500 and standard
deviation 60.
8. (1 point) What percent of the test takers have a score of 440 or less? Round answer to four places after
the decimal point.
9. (1 point) What percent of the test takers have a score of 590 or more? Round answer to four places
after the decimal point.
10. (1 point) What percent of the test takers have a score between 440 and 590? Round answer to four
places after the decimal point.
11. (1 point) Suppose a college will only admit students who score in the top 20% among all test takers,
what will be the minimum required score be? Round answer to the nearest whole number.
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
============
Suppose the scores of certain standardized tests are normally distributed with mean 500 and standard deviation 60.
8. (1 point) What percent of the test takers have a score of 440 or less? Round answer to four places after the decimal point.
----
z(440) = (440-500)/60 = -1
%(x <= 440) = %(z <= -1) = normalcdf(-1,100) = 84.1345
==============================================================
9. (1 point) What percent of the test takers have a score of 590 or more? Round answer to four places after the decimal point.
-----
Use the same process as above:
Ans: 6.6807
---------------------------
10. (1 point) What percent of the test takers have a score between 440 and 590? Round answer to four places after the decimal point.
%(440 < x < 590) = %(-1 < z < 1.5) = normalcdf(-1,1.5) = 77.4538
======================================
11. (1 point) Suppose a college will only admit students who score in the top 20% among all test takers, what will be the minimum required score be? Round answer to the nearest whole number.
---
Find the z-value with a left tail of 80% = invNorm(0.8) = 0.8416
---
Find the correspond score (x) using x = zs + u
x = 0.8416*60+400 = 550.50
===================================
cheers,
Stan H.

Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
8.
z=(440-500)/60=-60/60=-1
.1587=15.87% of the test takers have a score of 440 or less.
.
11.
Above .20 is 0.8416
z=0.8416=(x-500)/60
x-500=80.496
x=580.496=580
.
Ed