the soccer balls manufactured at a factory have pressures that are normally distributed, with a mean…

the soccer balls manufactured at a factory have pressures that are normally distributed, with a mean pressure of 8.7 psi and a standard deviation of 0.2 psi. what percentage of soccer balls from the factory have a pressure between 8.1 and 8.7 psi? 0.3% 49.85% 50% 99.7%

the soccer balls manufactured at a factory have pressures that are normally distributed, with a mean pressure of 8.7 psi and a standard deviation of 0.2 psi. what percentage of soccer balls from the factory have a pressure between 8.1 and 8.7 psi? 0.3% 49.85% 50% 99.7%

Answer

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $x = 8.1$, $z_1=\frac{8.1 - 8.7}{0.2}=\frac{- 0.6}{0.2}=-3$. For $x = 8.7$, $z_2=\frac{8.7 - 8.7}{0.2}=0$.

Step2: Use the standard normal distribution table

The standard - normal distribution table gives the cumulative probability $P(Z\lt z)$. $P(Z\lt - 3)=0.0015$ and $P(Z\lt0)=0.5$. The probability $P(-3\lt Z\lt0)=P(Z\lt0)-P(Z\lt - 3)$. $P(-3\lt Z\lt0)=0.5 - 0.0015 = 0.4985$.

Step3: Convert to percentage

To convert the probability to a percentage, multiply by 100. $0.4985\times100 = 49.85%$.

Answer:

49.85%