Answer:
1)
If the manufacturer's assumptions are correct, it would need to replace 8.23% of its batteries free of charge.
Option a) 8.23% is the correct option
2)
the required standard deviation is 3.8
Option a) 3.8 is the correct answer
Explanation:
Given the data in the question;
mean μ = 44
standard deviation σ = 3.6
if a battery fails within 39 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 39 months but within 50 months
1)
If the manufacturer's assumptions are correct, it would need to replace_____ of its batteries free of charge
p( X < 39 ) = P( X-μ/σ < 39-μ/σ )
we substitute
= p( Z < ((39-44)/3.6 ))
= p( Z < -1.39 )
from standard normal table; p( Z < -1.39 ) = 0.08226 ≈ 0.0823
p( X < 39 ) = 0.0823 or 8.23%
Therefore, If the manufacturer's assumptions are correct, it would need to replace 8.23% of its batteries free of charge.
Option a) 8.23% is the correct option
2)
The company finds that it s replacing 9.34% of its batteries free of charge. It suspects that its assumption about the standard deviation of the life of its batteries is incorrect. A standard deviation of ______ results in a 9.34% replacement rate.
given that;
P( Z < x-μ/σ ) = 9.34%
⇒ P( Z < 39-44/σ ) = 0.0934 ----- let this be equation 1
now, from standard normal tables
∅( -1.32 ) = 0.0934 ---------- let this equation 2
so from equation 1 and 2
39-44/σ = -132
-5/σ = -1.32
σ = -5 / - 1.32
σ = 3.7879 ≈ 3.8
Therefore, the required standard deviation is 3.8
Option a) 3.8 is the correct answer
