<u><em>The probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is 32.22%</em></u>
<u><em></em></u>
<u><em>Given here,</em></u>
<u><em></em></u>
<u><em>Mean (μ) = 3 years 6 months</em></u>
<u><em></em></u>
<u><em>= (3×12)+6 = 42 months</em></u>
<u><em></em></u>
<u><em>Standard deviation (σ) = 9 months</em></u>
<u><em></em></u>
<u><em>We will find the z-score using the formula: z = (X - μ)/σ</em></u>
<u><em></em></u>
<u><em>Here X₁ = 2 years 3 months</em></u>
<u><em></em></u>
<u><em>= (2×12)+3 = 27 months</em></u>
<u><em></em></u>
<u><em>and X₂ = 3 years 3 months</em></u>
<u><em></em></u>
<u><em>= (3×12)+3 = 39 months</em></u>
<u><em></em></u>
<u><em>So, z (X₁ =27) = </em></u>
<u><em></em></u>
<u><em>and z (X₂ =39) = </em></u>
<u><em></em></u>
<u><em>According to the standard normal table,</em></u>
<u><em></em></u>
<u><em>P(z> -1.666...) = 0.0485 and P(z< -0.333...) = 0.3707</em></u>
<u><em></em></u>
<u><em>So, P(27 < X < 39)</em></u>
<u><em></em></u>
<u><em>= 0.3707 - 0.0485</em></u>
<u><em></em></u>
<u><em>= 0.3222</em></u>
<u><em></em></u>
<u><em>= 32.22 % [Multiplying by 100 for getting percentage]</em></u>
<u><em></em></u>
- <u><em>So, the probability of a randomly selected hard drive from the company lasting between 2 years 3 months and 3 years 3 months is 32.22%</em></u>