Question Type 2: Finding mean and standard deviation given probability and x value Bootcamps

Let product lifetimes $X\sim N(1000,\sigma^2)$. Given $P(X<900)=0.1587$, find $\sigma$.

Let $X\sim N(27,\sigma^2)$. Given $P(X>32)=0.16$, find the variance of $X$.

Let $X\sim N(40,\sigma^2)$. Given $P(X<45)=0.95$, find $\sigma$.

Let heights $X\sim N(170,\sigma^2)$. If only 2.5% of adults exceed 190 cm, find $\sigma$.

Let $X\sim N(100,\sigma^2)$. Given $P(X>120)=0.10$, find the variance of $X$.

Let measurement errors $X\sim N(\mu,25)$. Given $P(X>20)=0.025$, find $\mu$.

Let $X\sim N(\mu,15^2)$. Given $P(X>60)=0.05$, find $\mu$.

Let $X\sim N(80,\sigma^2)$. Given $P(X>100)=0.025$, find $\sigma$.

Let test scores $X\sim N(\mu,10^2)$. Given $P(X<85)=0.84$, find $\mu$.

Let $X\sim N(\mu,20^2)$. Given $P(X<150)=0.10$, find $\mu$.

Let $X\sim N(\mu,\sigma^2)$. Given $P(X<5)=0.1587$ and $P(X>9)=0.1587$, find $\mu$ and $\sigma$.

Let $X\sim N(50,\sigma^2)$. Given $P(40<X<60)=0.95$, find $\sigma$.