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a.
For this to make sense, we will plot the bell curve of the distribution.
It is general convention that:
65% of the values in the distribution lie between
[tex]\begin{gathered} \bar{x}\pm\sigma \\ Where\colon \\ \bar{x}=\text{mean} \\ \sigma=s\tan dard\text{ deviation} \end{gathered}[/tex][tex]\begin{gathered} 48\pm3=51\text{ or 45} \\ \text{This means that }65\text{ \% of the values lie within the range 45 and 51.} \\ Therefore,\text{ the range between 48 and 51 will be a half of 65\%} \\ \frac{65}{2}\text{ \% = 32.5\%} \end{gathered}[/tex]35% is the percentage of cars that remain in service between 48 and 51 months
b.
We also plot the distribution curve as in a above,
[tex]\begin{gathered} 64\pm7=71\text{ or }57 \\ \text{This means that }65\text{ \% of the values lie within the range 57 and 71.} \\ Therefore,\text{ the range between 57 and 64 will be a half of 65\%} \\ \frac{65}{2}\text{ \% = 32.5\%} \end{gathered}[/tex]
32.5% is the approximate percentage of lightbulb replacement requests numbering between 57 and 64
