Answer:
The probability that Delta car batteries last between three and four years
P(36≤X≤48) = 0.5188
The percentage of that Delta car batteries last between three and four years
P(3≤X≤4) = 52%
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given that the sample size n =12 -volt car batteries</em>
<em>Let 'X' be a Random variable in a normal distribution</em>
<em>Given that mean of the normal distribution = 45 months</em>
<em>Given that the Standard deviation of the normal distribution = 8months</em>
<u><em>Step(ii):-</em></u>
Let X₁ = 3 years = 12 × 3 = 36 months
Let X₂ = 4 years = 12 × 4 = 48 months
<u><em>Step(iii)</em></u>:-
The probability that Delta car batteries last between three and four years
P(36≤X≤48) = P(-1.125≤Z≤0.375)
= P(Z≤0.375) - P(Z≤-1.125)
= 0.5 +A(0.375) - (0.5-A(1.125)
= 0.5 + 0.1480 - (0.5 -0.3708)
= 0.1480 + 0.3708
= 0.5188
<u><em>Final answer:-</em></u>
The probability that Delta car batteries last between three and four years
P(36≤X≤48) = 0.5188
The percentage of that Delta car batteries last between three and four years
P(3≤X≤4) = 52%
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