keeping car tires inflated is essential to safe driving. for one type of car tire, the tire pressure in…

keeping car tires inflated is essential to safe driving. for one type of car tire, the tire pressure in pounds per square inch (psi) is assumed to be approximately normal, with a mean of 35 psi and a standard deviation of 2 psi. what percentage of tires are inflated to a pressure between 33.5 and 36 psi? find the z - table here. 22.55% 46.48% 53.52% 77.45%

keeping car tires inflated is essential to safe driving. for one type of car tire, the tire pressure in pounds per square inch (psi) is assumed to be approximately normal, with a mean of 35 psi and a standard deviation of 2 psi. what percentage of tires are inflated to a pressure between 33.5 and 36 psi? find the z - table here. 22.55% 46.48% 53.52% 77.45%

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 $x = 33.5$, $z_1=\frac{33.5 - 35}{2}=\frac{- 1.5}{2}=-0.75$. For $x = 36$, $z_2=\frac{36 - 35}{2}=\frac{1}{2}=0.5$.

Step2: Use the z - table

We want to find $P(-0.75<Z<0.5)$. From the z - table, $P(Z < 0.5)=0.6915$ and $P(Z<-0.75) = 0.2266$. Then $P(-0.75<Z<0.5)=P(Z < 0.5)-P(Z<-0.75)$. $P(-0.75<Z<0.5)=0.6915 - 0.2266=0.4649\approx46.48%$.

Answer:

46.48%