A fair cube is colored so that 4 faces are green and 2 are red. The cube is tossed 9 times. If success is defined as a red face being up, find (a) the mean number of red faces and (b) the standard deviation of the number of red faces that occur.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 2CYU
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A fair cube is colored so that 4 faces are green and 2 are red. The cube is tossed 9 times. If success is defined as a red face being up, find

(a) the mean number of red faces and

(b) the standard deviation of the number of red faces that occur.

 

Expert Solution
Step 1

Given:

Number of red faces  = 2

Number of green faces = 4

Total number of faces = 2 + 4 

                                   = 6

Number rolls (n) = 9

P (success) = p = 26

Let X be the binomial random variable representing the number of times red face appears.

X~Bin9, 26

Step 2

a)

Mean of X

EX=n×p          =9×26          =3

The mean number of red faces is 3

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