for a brand, the life of light bulbs (b) are normally distributed with a mean of 750 hours and a standard…

Explanation:

Step1: Identify the number of standard - deviations from the mean

The mean $\mu = 750$ and the standard deviation $\sigma=75$. For $x = 675$, the z - score $z_1=\frac{675 - 750}{75}=\frac{- 75}{75}=-1$. For $x = 900$, the z - score $z_2=\frac{900 - 750}{75}=\frac{150}{75}=2$.

Step2: Apply the 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule states that:

• Approximately 68% of the data lies within 1 standard deviation of the mean ($\mu\pm\sigma$), approximately 95% lies within 2 standard deviations of the mean ($\mu\pm2\sigma$), and approximately 99.7% lies within 3 standard deviations of the mean ($\mu\pm3\sigma$). The area between $z=-1$ and $z = 2$ can be found by considering the areas of the standard normal distribution. The area between $z=- 1$ and $z = 1$ is 68%, and the area between $z = 1$ and $z = 2$ is half of the area between $z=-2$ and $z = 2$ minus the area between $z=-1$ and $z = 1$. The area between $z=-2$ and $z = 2$ is 95%, so the area between $z = 1$ and $z = 2$ is $\frac{95 - 68}{2}=13.5%$. The area between $z=-1$ and $z = 2$ is $68%+13.5% = 81.5%$.

Answer:

81.5%