Question

Question 1. Find the mean E(X) and the standard deviation \sigma σ for the following grade distribution:

Grade / GPA Proportion

A = 4 12%

B = 3 18%

C = 2 45%

D = 1 20%

F = 0 5%

Choose from group of answers below:

mean = 2.12, s.d. = 1.02

mean = 2.00, s.d. = 1.41

mean = 2.75, s.d. = 0.85   

mean = 2.50, s.d. = 1.15

Question 2. A small business finds that the probability of an employee getting caught stealing office supplies is about 7%. Out of an office of 15 employees, what is the probability that no employees are caught?

Choose from group of answers below:

1.05

4.75 E-18

0.2236

0.3367

Answer 1

Solution:

Question 1)

Find the mean E(X) and the standard deviation σ for the following grade distribution:

where

Grade	X: GPA	P(X): Proportion	X*P(X)	X2 *P(X)
A	4	12%	0.48	1.92
B	3	18%	0.54	1.62
C	2	45%	0.9	1.8
D	1	20%	0.2	0.2
F	0	5%	0	0

Thus

and

where

Thus

Thus correct answer is:

mean = 2.12, s.d. = 1.02

Question 2)

Given:

p = the probability of an employee getting caught stealing office supplies

p = 7% = 0.07

n = 15

Find the probability that no employees are caught.

that is find:

P(X = 0) =..........?

Binomial probability formula :

Where q = 1 – p = 1 - 0.07 = 0.93

thus