900 = 750 + 2*75. In other words, 900 is 2 standard deviations away from the mean. Similarly, 975 is 3 standard deviations from the mean. So[tex]P(900<X<975)=P(2<Z<3)[/texwhere [tex]X[/tex] is the random variable for the lifespan of a light bulb with the given normal distribution, and [tex]Z=\dfrac{X-750}{75}[/tex] with the standard normal distribution.We get[tex]P(2<Z<3)\approx0.0214=2.14\%[/tex]If you don't have a calculator/lookup table available, you can invoke the empirical rule, the one that says[tex]\begin{cases}P(-1<Z<1)\approx68\%\\P(-2<Z<2)\approx95\%\\P(-3<Z<3)\approx99.7\%\end{cases}[/tex]The normal distribution is symmetric about its mean, so we also know[tex]\begin{cases}P(0<Z<1)\approx34\%\\P(0<Z<2)\approx47.5\%\\P(0<Z<3)\approx49.85\%\end{cases}[/tex]Then[tex]P(2<Z<3)=P(0<Z<3)-P(0<Z<2)\approx2.35\%[/tex]