ng.c CASEY 2/10 Correct Question 3 of 10, Step 1 of 1 A humanities professor ass

Question

ng.c CASEY 2/10 Correct Question 3 of 10, Step 1 of 1 A humanities professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 63% scores below the top 37% and above the bottom 24% D: Scores below the top 76% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 72.9 and a standard deviation of 8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary Standard Normal Table-oo to-z Standard Normal Table-co to: © 2017 Hawkes Learning

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 72.9
standard Deviation ( sd )= 8
a.
P ( Z > x ) = 0.12
Value of z to the cumulative probability of 0.12 from normal table is 1.175
P( x-u / (s.d) > x - 72.9/8) = 0.12
That is, ( x - 72.9/8) = 1.175
--> x = 1.175 * 8+72.9 = 82.2999 ~ 83
b.
UPPER/TOP
P ( Z > x ) = 0.12
Value of z to the cumulative probability of 0.12 from normal table is 1.175
P( x-u / (s.d) > x - 72.9/8) = 0.12
That is, ( x - 72.9/8) = 1.175
--> x = 1.175 * 8+72.9 = 82.2999 ~ 82

LOWER/BELOW
P ( Z < x ) = 0.63
Value of z to the cumulative probability of 0.63 from normal table is 0.3319
P( x-u/s.d < x - 72.9/8 ) = 0.63
That is, ( x - 72.9/8 ) = 0.3319
--> x = 0.3319 * 8 + 72.9 = 75.5548 ~ 76

c.
UPPER/TOP
P ( Z > x ) = 0.24
Value of z to the cumulative probability of 0.24 from normal table is 0.7063
P( x-u / (s.d) > x - 72.9/8) = 0.24
That is, ( x - 72.9/8) = 0.7063
--> x = 0.7063 * 8+72.9 = 78.5504 ~ 79

LOWER/BELOW
P ( Z < x ) = 0.37
Value of z to the cumulative probability of 0.37 from normal table is -0.3319
P( x-u/s.d < x - 72.9/8 ) = 0.37
That is, ( x - 72.9/8 ) = -0.3319
--> x = -0.3319 * 8 + 72.9 = 70.2452 ~ 70

d.
UPPER/TOP
P ( Z > x ) = 0.76
Value of z to the cumulative probability of 0.76 from normal table is -0.7063
P( x-u / (s.d) > x - 72.9/8) = 0.76
That is, ( x - 72.9/8) = -0.7063
--> x = -0.7063 * 8+72.9 = 67.2496 ~ 67

LOWER/BELOW
P ( Z < x ) = 0.06
Value of z to the cumulative probability of 0.06 from normal table is -1.5548
P( x-u/s.d < x - 72.9/8 ) = 0.06
That is, ( x - 72.9/8 ) = -1.5548
--> x = -1.5548 * 8 + 72.9 = 60.4618 ~ 60

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.