Question

Best Electronics offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 9.6 per day and the standard deviation is 2.30 per day. Refer to the table in Appendix B.1.  

a. In what percentage of the days 6 or fewer customers returning items? (Round z-score computation to 2 decimal places and the final answer to 2 decimal places.)

Percentage            %

b. In what percentage of the days between 12 and 15 customers returning items? (Round z-score computation to 2 decimal places and the final answer to 2 decimal places.)

Percentage            %

c. Is there any chance of a day with no returns?

(Click to select)  

Answer 1

Part a)

X ~ N ( µ = 9.6 , σ = 2.3 )
P ( X <= 6 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 6 - 9.6 ) / 2.3
Z = -1.57
P ( ( X - µ ) / σ ) < ( 6 - 9.6 ) / 2.3 )
P ( X <= 6 ) = P ( Z < -1.57 )
P ( X <= 6 ) = 0.0582

Percentage = 0.0582 * 100 = 5.82%

Part b)

X ~ N ( µ = 9.6 , σ = 2.3 )
P ( 12 < X < 15 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 12 - 9.6 ) / 2.3
Z = 1.04
Z = ( 15 - 9.6 ) / 2.3
Z = 2.35
P ( 1.04 < Z < 2.35 )
P ( 12 < X < 15 ) = P ( Z < 2.35 ) - P ( Z < 1.04 )
P ( 12 < X < 15 ) = 0.9906 - 0.8508
P ( 12 < X < 15 ) = 0.1398
Percentage = 0.1398 * 100 = 13.98%

Part b)

Part c)

X ~ N ( µ = 9.6 , σ = 2.3 )
P ( X < 0 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 0 - 9.6 ) / 2.3
Z = -4.17
P ( ( X - µ ) / σ ) < ( 0 - 9.6 ) / 2.3 )
P ( X < 0 ) = P ( Z < -4.17 )
P ( X < 0 ) = 0
It is impossible event, since probability is 0.