? ck start company makes 12 vot car batteres. After many years cf produt testing

Question

? ck start company makes 12 vot car batteres. After many years cf produt testing, the company irows that the rmage ite of,Oasn battery rormally diebuted,-th , me·d46imees aed "the-d deuen of 9.3 months a) I, batteries wa·be pay e ped to d your er be b een ce uick Start gu rantees·f" refund on any battery that teas-thin the orth perod after purchase, what percentage of 1%ofts batteries under the f A-mfund gerantee ·for ho.og nad onpary panntee the battern the nered month (b) If Quick Start does not want to make refunds for more than 1

Explanation / Answer

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(X < 36) = P(Z < (36 - 46.6)/9.3)

= P(Z < -1.14)

= 0.1271

b) Let the company offer guarantee for M months

P(X < M) = P(Z < (M - 46.6)/9.3) = 0.11

(M - 46.6)/9.3 = -1.23

M = 35.16

= 35 months

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